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On the Bifurcation From Continuous to Segmented Chip Formation in Metal Cutting



Timothy J. Burns, Matthew A. Davies, Christopher J. Evans


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


adiabatic shear bands, machining, plsticity, relaxation oscillations, singular Hopf bifurcation


Burns, T. , Davies, M. and Evans, C. (2000), On the Bifurcation From Continuous to Segmented Chip Formation in Metal Cutting, IMA Volumes in Mathematics and its Applications, University of MN, MN (Accessed June 22, 2024)


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Created February 6, 2000, Updated February 19, 2017