An alternative approach for the analytical study of nonlinear machine-tool chatter

摘要

Machine-tool chatter is a highly coupled and nonlinear dynamic problem with a large chip deformation process during which frictional, periodic and irregular micro-structural characteristics will be induced by regenerative and non-regenerative time delay forces. Evidence in the literature has shown that there are traces of multiple regenerative chatter, which can produce distinctive marks on the cutting tool and workpiece. Furthermore, in the regions of linearized stability through a single Hopf bifurcation, there now exists evidence of low levels of chaotic and/or stochastic dynamics. These observations and many more intriguing mechanisms of machine-tool chatter have inspired a growing interest in search of effective analytical and experimental techniques. The centre manifold reduction at Hopf bifurcation currently stands alone in the mathematical literature as the most valid way to reduce the infinite-dimensional character of delay differential equations into finite-dimensional ODEs and at the same time maintaining the dynamics of the original system. It is therefore felt that this approach could be a natural framework for the characterization of chatter instability and their resulting dynamic phenomena for lower and higher dimensional situations.