Estimates of the bistable region in metal cutting

Zoltan Dombovari*, R. Eddie Wilson, Gabor Stepan

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

56 Citations (Scopus)


The classical model of regenerative vibration is investigated with new kinds of nonlinear cutting force characteristics. The standard nonlinear characteristics are subjected to a critical review from the nonlinear dynamics viewpoint based on the experimental results available in the literature. The proposed nonlinear model includes finite derivatives at zero chip thickness and has an essential inflexion point. In the case of the one degree-of-freedom model of orthogonal cutting, the existence of unstable self-excited vibrations is proven along the stability limits, which is strongly related to the force characteristic at its inflexion point. An analytical estimate is given for a certain area below the stability limit where stable stationary cutting and a chaotic attractor coexist. It is shown how this domain of bistability depends on the theoretical chip thickness. The comparison of these results with the experimental observations and also with the subcritical Hopf bifurcation results obtained for standard nonlinear cutting force characteristics provides relevant information on the nature of the cutting force nonlinearity.

Original languageEnglish
Pages (from-to)3255-3271
Number of pages17
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2100
Publication statusPublished - 8 Dec 2008

Structured keywords

  • Engineering Mathematics Research Group


  • subcritical
  • Hopf bifurcation
  • limit cycle
  • metal cutting
  • bistable zones
  • turning


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