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)
Gaithersburg
Wednesday, October 22, 2003 13:00-14:00,
Room 4550
Boulder
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. KearsleyNote: Visitors from outside NIST must contact
Robin Bickel; (301) 975-3668;
at least 24 hours in advance.
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