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Limit cycles, bifurcations, and accuracy of the milling process

Publication ,  Journal Article
Mann, BP; Bayly, PV; Davies, MA; Halley, JE
Published in: Journal of Sound and Vibration
October 6, 2004

Time finite element analysis (TFEA) is used to determine the accuracy, stability, and limit cycle behavior of the milling process. Predictions are compared to traditional Euler simulation and experiments. The TFEA method forms an approximate solution by dividing the time in the cut into a finite number of elements. The approximate solution is then matched with the exact solution for free vibration to obtain a discrete linear map. Stability is then determined from the characteristic multipliers of the map. Map fixed points correspond to stable periodic solutions which are used to evaluate surface location error. Bifurcations and limit cycle behavior are predicted from a non-linear TFEA formulation. Experimental cutting tests are used to confirm theoretical predictions. © 2003 Elsevier Ltd. All rights reserved.

Duke Scholars

Published In

Journal of Sound and Vibration

DOI

ISSN

0022-460X

Publication Date

October 6, 2004

Volume

277

Issue

1-2

Start / End Page

31 / 48

Related Subject Headings

  • Acoustics
  • 51 Physical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
 

Citation

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ICMJE
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Mann, B. P., Bayly, P. V., Davies, M. A., & Halley, J. E. (2004). Limit cycles, bifurcations, and accuracy of the milling process. Journal of Sound and Vibration, 277(1–2), 31–48. https://doi.org/10.1016/j.jsv.2003.08.040
Mann, B. P., P. V. Bayly, M. A. Davies, and J. E. Halley. “Limit cycles, bifurcations, and accuracy of the milling process.” Journal of Sound and Vibration 277, no. 1–2 (October 6, 2004): 31–48. https://doi.org/10.1016/j.jsv.2003.08.040.
Mann BP, Bayly PV, Davies MA, Halley JE. Limit cycles, bifurcations, and accuracy of the milling process. Journal of Sound and Vibration. 2004 Oct 6;277(1–2):31–48.
Mann, B. P., et al. “Limit cycles, bifurcations, and accuracy of the milling process.” Journal of Sound and Vibration, vol. 277, no. 1–2, Oct. 2004, pp. 31–48. Scopus, doi:10.1016/j.jsv.2003.08.040.
Mann BP, Bayly PV, Davies MA, Halley JE. Limit cycles, bifurcations, and accuracy of the milling process. Journal of Sound and Vibration. 2004 Oct 6;277(1–2):31–48.
Journal cover image

Published In

Journal of Sound and Vibration

DOI

ISSN

0022-460X

Publication Date

October 6, 2004

Volume

277

Issue

1-2

Start / End Page

31 / 48

Related Subject Headings

  • Acoustics
  • 51 Physical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences