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Dynamics of milling processes with variable time delays

Publication ,  Journal Article
Long, XH; Balachandran, B; Mann, BP
Published in: Nonlinear Dynamics
January 1, 2007

A milling-process model with a variable time delay associated with each cutting tooth is presented in this article. The source of this variable time delay is the feed rate. The effect of the feed motion on the entry cutting angle, the exit cutting angle, and the amplitude of feed mark is also discussed. Loss-of-contact effects are also considered. The system dynamics is described by a set of delay differential equations with periodic coefficients and variable time delays. A semi-discretization scheme is presented for analyzing the stability of periodic orbits of this system. The analysis provides evidence of period-doubling bifurcations and secondary Hopf bifurcations. Good agreement is found between the numerical results obtained from this work and the results of related experimental studies. © Springer Science+Business Media, Inc. 2007.

Duke Scholars

Published In

Nonlinear Dynamics

DOI

ISSN

0924-090X

Publication Date

January 1, 2007

Volume

47

Issue

1-3

Start / End Page

49 / 63

Related Subject Headings

  • Acoustics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences
 

Citation

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Long, X. H., Balachandran, B., & Mann, B. P. (2007). Dynamics of milling processes with variable time delays. Nonlinear Dynamics, 47(1–3), 49–63. https://doi.org/10.1007/s11071-006-9058-4
Long, X. H., B. Balachandran, and B. P. Mann. “Dynamics of milling processes with variable time delays.” Nonlinear Dynamics 47, no. 1–3 (January 1, 2007): 49–63. https://doi.org/10.1007/s11071-006-9058-4.
Long XH, Balachandran B, Mann BP. Dynamics of milling processes with variable time delays. Nonlinear Dynamics. 2007 Jan 1;47(1–3):49–63.
Long, X. H., et al. “Dynamics of milling processes with variable time delays.” Nonlinear Dynamics, vol. 47, no. 1–3, Jan. 2007, pp. 49–63. Scopus, doi:10.1007/s11071-006-9058-4.
Long XH, Balachandran B, Mann BP. Dynamics of milling processes with variable time delays. Nonlinear Dynamics. 2007 Jan 1;47(1–3):49–63.
Journal cover image

Published In

Nonlinear Dynamics

DOI

ISSN

0924-090X

Publication Date

January 1, 2007

Volume

47

Issue

1-3

Start / End Page

49 / 63

Related Subject Headings

  • Acoustics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences