In this paper, a new method for the stability analysis of interrupted turning 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 is substituted into the characteristic function, leading to an implicit formula for 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.
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July 2006
Research Papers
Lobes and Lenses in the Stability Chart of Interrupted Turning
Róbert Szalai
,
szalai@mm.bme.hu
Róbert Szalai
Graduate Student
Budapest University of Technology and Economics
, Budapest, H-1521, Hungary
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Gábor Stépán
stepan@mm.bme.hu
Gábor Stépán
Professor Head of Department of Applied Mechanics
Budapest University of Technology and Economics
, Budapest, H-1521, Hungary
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Róbert Szalai
Graduate Student
Gábor Stépán
Professor Head of Department of Applied Mechanics
J. Comput. Nonlinear Dynam. Jul 2006, 1(3): 205-211 (7 pages)
Published Online: November 15, 2003
Article history
Online:
November 15, 2003
Online:
November 21, 2003
Received:
August 20, 2005
Revised:
February 15, 2006
Citation
Szalai, R., and Stépán, G. (November 15, 2003). "Lobes and Lenses in the Stability Chart of Interrupted Turning." ASME. J. Comput. Nonlinear Dynam. July 2006; 1(3): 205–211. https://doi.org/10.1115/1.2198216
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