Characterization of nonlinearity of cutting tool vibrations and chatter

Chatter control in turning is a problem of immense engineering importance because the occurrence of chatter harms the workpiece, the machine tool and the workplace. Most existing chatter control paradigms are based on the linear viewpoint of chatter, according to which the occurrence of chatter may be attributed mainly to (i) regenerative effects, and (ii) mode coupling. Finite amplitude chatter, even with negligible viscous damping, was not incorporated in early works. Other phenomena - such as multiple chatter modes, uncertainty of chatter, and absence of clear stability boundaries - have not been considered in the existing control paradigms. This may be because these phenomena cannot be explained without resorting to nonlinear dynamics. In this paper, we propose a nonlinear theory of cutting tool vibrations with special emphasis on chatter which overcomes many shortcomings of the linear viewpoint. Based on this theory, we develop a piecewise model that accounts for different parametric bifurcations and sensitivity to initial conditions with just two degrees of freedom. We anticipate that this model will be used for chatter control based on the principles of gain scheduling.