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Milling bifurcations from structural asymmetry and nonlinear regeneration

Publication ,  Journal Article
Mann, BP; Garg, NK; Young, KA; Helvey, AM
Published in: Nonlinear Dynamics
December 1, 2005

This paper investigates multiple modeling choices for analyzing the rich and complex dynamics of high-speed milling processes. Various models are introduced to capture the effects of asymmetric structural modes and the influence of nonlinear regeneration in a discontinuous cutting force model. Stability is determined from the development of a dynamic map for the resulting variational system. The general case of asymmetric structural elements is investigated with a fixed frame and rotating frame model to show differences in the predicted unstable regions due to parametric excitation. Analytical and numerical investigations are confirmed through a series of experimental cutting tests. The principal results are additional unstable regions, hysteresis in the bifurcation diagrams, and the presence of coexisting periodic and quasiperiodic attractors which is confirmed through experimentation. © Springer 2005.

Duke Scholars

Published In

Nonlinear Dynamics

DOI

ISSN

0924-090X

Publication Date

December 1, 2005

Volume

42

Issue

4

Start / End Page

319 / 337

Related Subject Headings

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

Citation

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Mann, B. P., Garg, N. K., Young, K. A., & Helvey, A. M. (2005). Milling bifurcations from structural asymmetry and nonlinear regeneration. Nonlinear Dynamics, 42(4), 319–337. https://doi.org/10.1007/s11071-005-5719-y
Mann, B. P., N. K. Garg, K. A. Young, and A. M. Helvey. “Milling bifurcations from structural asymmetry and nonlinear regeneration.” Nonlinear Dynamics 42, no. 4 (December 1, 2005): 319–37. https://doi.org/10.1007/s11071-005-5719-y.
Mann BP, Garg NK, Young KA, Helvey AM. Milling bifurcations from structural asymmetry and nonlinear regeneration. Nonlinear Dynamics. 2005 Dec 1;42(4):319–37.
Mann, B. P., et al. “Milling bifurcations from structural asymmetry and nonlinear regeneration.” Nonlinear Dynamics, vol. 42, no. 4, Dec. 2005, pp. 319–37. Scopus, doi:10.1007/s11071-005-5719-y.
Mann BP, Garg NK, Young KA, Helvey AM. Milling bifurcations from structural asymmetry and nonlinear regeneration. Nonlinear Dynamics. 2005 Dec 1;42(4):319–337.
Journal cover image

Published In

Nonlinear Dynamics

DOI

ISSN

0924-090X

Publication Date

December 1, 2005

Volume

42

Issue

4

Start / End Page

319 / 337

Related Subject Headings

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