Period doubling bifurcation and center manifold reduction in a time-periodic and time-delayed model of machining

Róbert Szalai, Gábor Stépán

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A closed-form calculation is presented for the analysis of the period-doubling bifurcation in the time-periodic delay-differential equation model of interrupted machining processes such as milling where the nonlinearity is essentially nonsymmetric. We prove the subcritical sense of this period-doubling bifurcation and approximate the emerging period-two oscillations by the Lyapunovg-Perron method for computing the center manifold and by calculating the Poincarég-Lyapunov constant of the bifurcation analytically at certain characteristic parameter values. The existence of the unstable period-two oscillations around the stable stationary cutting is confirmed using a numerical continuation algorithm developed for time-periodic delay-differential equations.

Original languageEnglish
Pages (from-to)1169-1187
Number of pages19
JournalJVC/Journal of Vibration and Control
Issue number7-8
Publication statusPublished - Jun 1 2010



  • Bifurcation
  • center manifold
  • high-speed milling
  • normal form
  • period doubling

ASJC Scopus subject areas

  • Automotive Engineering
  • Materials Science(all)
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering

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