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Stability Boundaries of High-Speed Milling Corresponding to Period Doubling Are Essentially Closed Curves

[+] Author Affiliations
Róbert Szalai, Gábor Stépán

Budapest University of Technology and Economics, Budapest, Hungary

Paper No. IMECE2003-42122, pp. 63-68; 6 pages
doi:10.1115/IMECE2003-42122
From:
  • ASME 2003 International Mechanical Engineering Congress and Exposition
  • Manufacturing
  • Washington, DC, USA, November 15–21, 2003
  • Conference Sponsors: Manufacturing Engineering Division
  • ISBN: 0-7918-3720-3 | eISBN: 0-7918-4663-6, 0-7918-4664-4, 0-7918-4665-2
  • Copyright © 2003 by ASME

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.

Copyright © 2003 by ASME
Topics: Stability , Milling

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