In this paper we present stability analysis of a non-linear model for chatter vibration in a drilling operation. The results build our previous work [Stone, E., and Askari, A., 2002, “Nonlinear Models of Chatter in Drilling Processes,” Dyn. Syst., 17(1), pp. 65–85 and Stone, E., and Campbell, S. A., 2004, “Stability and Bifurcation Analysis of a Nonlinear DDE Model for Drilling,” J. Nonlinear Sci., 14(1), pp. 27–57], where the model was developed and the nonlinear stability of the vibration modes as cutting width is varied was presented. Here we analyze the effect of varying cutting depth. We show that qualitatively different stability lobes are produced in this case. We analyze the criticality of the Hopf bifurcation associated with loss of stability and show that changes in criticality can occur along the stability boundary, resulting in extra periodic solutions.
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October 2006
Research Papers
Analysis of the Chatter Instability in a Nonlinear Model for Drilling
Sue Ann Campbell,
Sue Ann Campbell
Department of Applied Mathematics,
e-mail: sacampbell@uwaterloo.ca
University of Waterloo
, Waterloo, ON N2L 3G1 Canada
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Emily Stone
Emily Stone
Department of Mathematical Sciences,
The University of Montana
, Missoula, MT 59812
Search for other works by this author on:
Sue Ann Campbell
Department of Applied Mathematics,
University of Waterloo
, Waterloo, ON N2L 3G1 Canadae-mail: sacampbell@uwaterloo.ca
Emily Stone
Department of Mathematical Sciences,
The University of Montana
, Missoula, MT 59812J. Comput. Nonlinear Dynam. Oct 2006, 1(4): 294-306 (13 pages)
Published Online: April 20, 2006
Article history
Received:
November 15, 2005
Revised:
April 20, 2006
Citation
Campbell, S. A., and Stone, E. (April 20, 2006). "Analysis of the Chatter Instability in a Nonlinear Model for Drilling." ASME. J. Comput. Nonlinear Dynam. October 2006; 1(4): 294–306. https://doi.org/10.1115/1.2338648
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