Nonlinear Dynamics Models for High-Speed Machining
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.