Nonlinear Dynamics Models for High-Speed Machining
October 1997
High-speed machining processes are increasingly important in modern
manufacturing. However, such processes can lead to discontinuous chip formation
that is strongly correlated with increased tool wear, degradation of the
workpiece surface finish, and less accuracy in the machined part. ITL's
Mathematical and Computational Sciences Division is collaborating with
the Automated Production Technology Division, MEL, to develop a new approach
to modeling some high-speed machining processes that has the potential
to predict the onset of discontinuities.
ITL's Timothy Burns and MEL's Matthew Davies treated some basic metal
cutting operations as nonlinear dynamical systems that include a mechanism
for thermomechanical feedback in the region where the tooltip and workpiece
material are in contact. The resulting mathematical models share many similarities
with models of open chemical reactors. In a paper published in the Annals
of the C.I.R.P. (International Institution for Production Engineering Research),
co-authored with Christopher J. Evans of MEL's Precision Engineering Division,
Burns and Davies showed that, as the cutting speed is increased, a bifurcation
from steady-state to oscillatory behavior occurs in computer simulations
of the model, which is consistent with the change from continuous to segmented
chip formation.
To obtain an analytical criterion for the material and cutting conditions
at which this bifurcation occurs, the researchers developed a related but
simpler lumped-parameters model. In a paper in Physical Review Letters,
Burns and Davies demonstrated that a Hopf bifurcation provides a dimensionless
group of parameters directly proportional to the cutting speed that predicts
the onset of discontinuous chip formation, and is consistent with experimental
observations on hardened steel and copper. Improvements in the models are
in progress.
This research provides improved mathematical models for computer simulations
of manufacturing processes which involve high-speed cutting of materials.
Industry can use this information to control and improve the machining
processes.
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