High-speed milling is often modeled as a kind of highly interrupted machining, when the ratio of time spent cutting to not cutting can be considered as a small parameter. In these cases, the classical regenerative vibration model, playing an essential role in machine tool vibrations, breaks down to a simplified discrete mathematical model. The linear analysis of this discrete model leads to the recognition of the doubling of the so-called instability lobes in the stability charts of the machining parameters. This kind of lobe-doubling is related to the appearance of period doubling vibrations originated in a flip bifurcation. This is a new phenomenon occurring primarily in low-immersion high-speed milling along with the Neimark-Sacker bifurcations related to the classical self-excited vibrations or Hopf bifurcations. The present work investigates the nonlinear vibrations in the case of period doubling and compares this to the well-known subcritical nature of the Hopf bifurcations in turning processes. The identification of the global attractor in the case of unstable cutting leads to contradiction between experiments and theory. This contradiction draws the attention to the limitations of the small parameter approach related to the highly interrupted cutting condition.
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e-mail: stepan@mm.bme.hu
e-mail: szalai@mm.bme.hu
e-mail: janez.gradisek@fs.uni-lj.si
e-mail: ̱edvard.govekar@fs.uni-lj.si
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April 2005
Technical Papers
Nonlinear Dynamics of High-Speed Milling—Analyses, Numerics, and Experiments
Gabor Stepan,
Gabor Stepan
Department of Applied Mechanics,
e-mail: stepan@mm.bme.hu
Budapest University of Technology and Economics
, Budapest, H-1521, Hungary
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Robert Szalai,
Robert Szalai
Department of Applied Mechanics,
e-mail: szalai@mm.bme.hu
Budapest University of Technology and Economics
, Budapest, H-1521, Hungary
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Brian P. Mann,
Brian P. Mann
Department of Mechanical and Aerospace Engineering,
University of Florida
, Gainesville, FL 32611
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Philip V. Bayly,
Philip V. Bayly
Department of Mechanical Engineering,
Washington University
, St. Louis, MO 63130
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Tamas Insperger,
Tamas Insperger
Department of Applied Mechanics,
Budapest University of Technology and Economics
, Budapest, H-1521, Hungary
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Janez Gradisek,
Janez Gradisek
Laboratory of Synergetics,
e-mail: janez.gradisek@fs.uni-lj.si
University of Ljubljana
, Ljubljana, SI-1000, Slovenia
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Edvard Govekar
Edvard Govekar
Laboratory of Synergetics,
e-mail: ̱edvard.govekar@fs.uni-lj.si
University of Ljubljana
, Ljubljana, SI-1000, Slovenia
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Gabor Stepan
Department of Applied Mechanics,
Budapest University of Technology and Economics
, Budapest, H-1521, Hungarye-mail: stepan@mm.bme.hu
Robert Szalai
Department of Applied Mechanics,
Budapest University of Technology and Economics
, Budapest, H-1521, Hungarye-mail: szalai@mm.bme.hu
Brian P. Mann
Department of Mechanical and Aerospace Engineering,
University of Florida
, Gainesville, FL 32611
Philip V. Bayly
Department of Mechanical Engineering,
Washington University
, St. Louis, MO 63130
Tamas Insperger
Department of Applied Mechanics,
Budapest University of Technology and Economics
, Budapest, H-1521, Hungary
Janez Gradisek
Laboratory of Synergetics,
University of Ljubljana
, Ljubljana, SI-1000, Sloveniae-mail: janez.gradisek@fs.uni-lj.si
Edvard Govekar
Laboratory of Synergetics,
University of Ljubljana
, Ljubljana, SI-1000, Sloveniae-mail: ̱edvard.govekar@fs.uni-lj.si
J. Vib. Acoust. Apr 2005, 127(2): 197-203 (7 pages)
Published Online: June 10, 2004
Article history
Received:
December 23, 2003
Revised:
June 10, 2004
Citation
Stepan, G., Szalai, R., Mann, B. P., Bayly, P. V., Insperger, T., Gradisek, J., and Govekar, E. (June 10, 2004). "Nonlinear Dynamics of High-Speed Milling—Analyses, Numerics, and Experiments." ASME. J. Vib. Acoust. April 2005; 127(2): 197–203. https://doi.org/10.1115/1.1891818
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