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

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Author(s): Timothy J. Burns; Matthew A. Davies; Christopher J. Evans;
Title: On the Bifurcation From Continuous to Segmented Chip Formation in Metal Cutting
Published: February 06, 2000
Abstract: 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.
Conference: Numerical Methods for Bifurcation Problems
Proceedings: IMA Volumes in Mathematics and its Applications
Volume: 119
Pages: pp. 67 - 83
Location: University of MN, MN
Dates: September 15-17, 1997
Keywords: adiabatic shear bands;machining;plsticity;relaxation oscillations;singular Hopf bifurcation
Research Areas: Math