Estimates of the bistable region in metal cutting

Zoltan Dombovari, R. Eddie Wilson, G. Stépán

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

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
Volume464
Issue number2100
DOIs
Publication statusPublished - Dec 8 2008

Fingerprint

metal cutting
Metal cutting
Cutting Force
Metals
Point of inflection
estimates
inflection points
Estimate
Chip
Vibration
chips
Bistability
Chaotic Attractor
vibration
Hopf Bifurcation
Hopf bifurcation
Nonlinear Dynamics
Nonlinear Model
Unstable
Degree of freedom

Keywords

  • Bistable zones
  • Hopf bifurcation
  • Metal cutting
  • Subcritical
  • Turning;limit cycle

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

Cite this

Estimates of the bistable region in metal cutting. / Dombovari, Zoltan; Wilson, R. Eddie; Stépán, G.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 464, No. 2100, 08.12.2008, p. 3255-3271.

Research output: Contribution to journalArticle

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