ITLApplied  Computational Mathematics Division
ACMD Seminar Series
Attractive Image NIST

Subcritical Flip Bifurcation in High-Speed Machining

Tim Burns
Mathematical and Computational Sciences Division

Wednesday, October 22, 2003 15:00-16:00,
Room 145, NIST North (820)
Wednesday, October 22, 2003 13:00-14:00,
Room 4550

Abstract: When a machine tool works on a surface that has already been machined, as is often the case in practical metal-cutting operations, it is well known that the dynamic interaction of the tool with the wave left on the surface during previous cuts can cause unstable vibrations to evolve in the system. This type of self-excited tool oscillation is called regenerative chatter. Because chatter vibrations can cause poor surface finish on the workpiece and rapid wear on the cutting tool, much work has been done on the modeling and analysis of the dynamics of regenerative chatter in machining. The theory of delay-differential equations is typically required in these studies, to take into account the deformation history left on the workpiece during previous passes of the cutting tool. For the case of full-immersion machining operations such as slot milling, there have been a number of theoretical analyses, supported by experimental results. They predict that the most stable cutting speeds occur at integer fractions of the natural frequency of the system. Furthermore, it has been shown theoretically and verified experimentally that a subcritical Hopf bifurcation occurs when the system is held at a fixed cutting speed as the depth of cut is increased. In this talk, we present a theory we have developed for the study of chatter in highly-interrupted machining operations. These operations are becoming more prevalent in modern manufacturing applications, such as finish milling of thin components and cutting of overhung and suspended structures. Our theory makes the useful prediction that, in comparison to full-immersion milling, there is a doubling in the number of optimally stable cutting speeds. The original most-stable speeds are present as before, but additional most-stable cutting speeds appear at odd-integer multiples of a half-period of the most flexible mode of the cutting system. Furthermore, as the depth of cut is increased at a fixed cutting speed, we show that, together with the new most-stable speeds in the system, a new type of instability also appears: a subcritical flip bifurcation. We show that the predictions of the theory are supported by experiment and numerical simulation. Collaborators on this work include M.A. Davies, B. Dutterer, B.F. Feeny, Ming Liao, J.R. Pratt, and T.L. Schmitz.
Contact: A. J. Kearsley

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