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Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems pp 67–83Cite as

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

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 119))

Abstract

We describe a new approach to modeling chip formation in orthogonal machining. Metal cutting is interpreted as a nonlinear dynamical process with thermo-mechanical feedback, that 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 Poincaré-Andronov-Hopf bifurcation in the material flow.

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Author information

Authors and Affiliations

  1. Information Technology Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland, 20899, USA

    T. J. Burns

  2. Manufacturing Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland, 20899, USA

    M. A. Davies & C. J. Evans

Authors
  1. T. J. Burns
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  2. M. A. Davies
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  3. C. J. Evans
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Editor information

Editors and Affiliations

  1. Applied Math 217-50, California Institute of Technology, Pasadena, CA, 91125, USA

    Eusebius Doedel

  2. Laboratoire d’Informatique pour la Mécanique et les Sciences de l’Ingénieur (LIMSI), B.P. 133, 91403, Orsay, France

    Laurette S. Tuckerman

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Burns, T.J., Davies, M.A., Evans, C.J. (2000). On the Bifurcation from Continuous to Segmented Chip Formation in Metal Cutting. In: Doedel, E., Tuckerman, L.S. (eds) Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems. The IMA Volumes in Mathematics and its Applications, vol 119. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1208-9_3

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  • DOI: https://doi.org/10.1007/978-1-4612-1208-9_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7044-7

  • Online ISBN: 978-1-4612-1208-9

  • eBook Packages: Springer Book Archive

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