Delay, parametric excitation, and the nonlinear dynamics of cutting processes

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78 Citations (Scopus)


It is a rule of thumb that time delay tends to destabilize any dynamical system. This is not true, however, in the case of delayed oscillators, which serve as mechanical models for several surprising physical phenomena. Parametric excitation of oscillatory systems also exhibits stability properties sometimes defying our physical sense. The combination of the two effects leads to challenging tasks when nonlinear dynamic behaviors in these systems are to be predicted or explained as well. This paper gives a brief historical review of the development of stability analysis in these systems, induced by newer and newer models in several fields of engineering. Local and global nonlinear behavior is also discussed in the case of the most typical parametrically excited delayed oscillator, a recent model of cutting applied to the study of high-speed milling processes.

Original languageEnglish
Pages (from-to)2783-2798
Number of pages16
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number9
Publication statusPublished - Sep 2005


  • Cutting
  • Regenerative effect
  • Time delay
  • Time periodic systems

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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