We describe a new approach to modeling chip formation in orthogonal machining. Metal cutting is interpreted as a nonlinear dynamical process with thermomechanical feedback, which is similar in many ways to an open chemical reactor. As the cutting speed is increased, there is a bifurcation from steady-state to periodic oscillatory behavior in the stress and temperature fields in the workpiece material at the tooltip, which explains the observed change from continuous to segmented chip formation. We argue that this change in behavior corresponds to a singular Poincare-Andronov-Hopf bifurcation in the material flow.
Proceedings Title: IMA Volumes in Mathematics and its Applications
Conference Dates: September 15-17, 1997
Conference Location: University of MN, MN
Conference Title: Numerical Methods for Bifurcation Problems
Pub Type: Conferences
adiabatic shear bands, machining, plsticity, relaxation oscillations, singular Hopf bifurcation