The Chaotic Oscillations of High-Speed Milling

  • G. Stépán
  • R. Szalai
  • S. J. Hogan
Conference paper
Part of the Solid Mechanics and its Applications book series (SMIA, volume 122)


In case of highly interrupted machining, the ratio of time spent cutting to not cutting can be considered as a small parameter. In these cases, the classical regenerative vibration model playing an essential role in machine tool vibrations breaks down to a simplified discrete mathematical model. The linear analysis of this discrete model leads to the recognition of the doubling of the so-called instability lobes in the stability charts of the machining parameters. This kind of lobe doubling is related to the appearance of period doubling vibration or flip bifurcation. This is a new phenomenon occurring primarily in low-immersion high-speed milling along with the classical self-excited vibrations or secondary Hopf bifurcations. The present work investigates the nonlinear vibrations in case of period doubling and compares this to the well-known subcritical nature of the Hopf bifurcations in turning processes. Also, the appearance of chaotic oscillation ‘outside’ the unstable period-two oscillation is proved for low-immersion high-speed milling processes.

Key words

Flip bifurcation high-speed milling time delay 


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Copyright information

© Springer 2005

Authors and Affiliations

  • G. Stépán
    • 1
  • R. Szalai
    • 1
  • S. J. Hogan
    • 2
  1. 1.Department of Applied MechanicsBudapest University of Technology and EconomicsBudapestHungary
  2. 2.Department of Engineering MathematicsUniversity of BristolBristolEngland

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