Stability boundaries of high-speed milling corresponding to period doubling are essentially closed curves

Róbert Szalai, Gábor Stépán

Research output: Contribution to conferencePaper

20 Citations (Scopus)

Abstract

In this paper a new method for the stability analysis of high-speed milling processes is introduced. The approach is based on the construction of a characteristic function whose complex roots determine the stability of the system. By using the argument principle, the number of roots causing instability can be counted, and thus, an exact stability chart can be drawn. In the special case of period doubling bifurcation, the corresponding multiplier - 1 is substituted into the characteristic function leading to an implicit formula of the stability boundaries. Further investigations show that all the period doubling boundaries are closed curves, except the first lobe at the highest cutting speeds. Together with the stability boundaries of Neimark-Sacker (or secondary Hopf) bifurcations, the unstable parameter domains are formed from the union of lobes and lenses.

Original languageEnglish
Pages63-68
Number of pages6
DOIs
Publication statusPublished - Jan 1 2003
Event2003 ASME International Mechanical Engineering Congress - Washington, DC., United States
Duration: Nov 15 2003Nov 21 2003

Other

Other2003 ASME International Mechanical Engineering Congress
CountryUnited States
CityWashington, DC.
Period11/15/0311/21/03

ASJC Scopus subject areas

  • Engineering(all)

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    Szalai, R., & Stépán, G. (2003). Stability boundaries of high-speed milling corresponding to period doubling are essentially closed curves. 63-68. Paper presented at 2003 ASME International Mechanical Engineering Congress, Washington, DC., United States. https://doi.org/10.1115/IMECE2003-42122