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The classical model of regenerative vibration is investigated with new kinds of nonlinear cutting force characteristics. The standard nonlinear characteristics are subjected to a critical review from the nonlinear dynamics viewpoint based on the experimental results available in the literature. The proposed nonlinear model includes finite derivatives at zero chip thickness and has an essential inflexion point. In the case of the one degreeof-freedom model of orthogonal cutting, the existence of unstable self-excited vibrations is proven along the stability limits, which is strongly related to the force characteristic at its inflexion point. An analytical estimate is given for a certain area below the stability limit where stable stationary cutting and a chaotic attractor coexist. It is shown how this domain of bistability depends on the theoretical chip thickness. The comparison of these results with the experimental observations and also with the subcritical Hopf bifurcation results obtained for standard nonlinear cutting force characteristics provides relevant information on the nature of the cutting force nonlinearity.

The large-amplitude motions of a one degree-of-freedom model of orthogonal cutting are analysed. The model takes the form of a delay differential equation which is non-smooth at the instant at which the tool loses contact with the workpiece, and which is coupled to an algebraic equation that stores the profile of the cut surface whilst the tool is not in contact. This system is approximated by a smooth delay differential equation without algebraic effects which is analysed with numerical continuation software. The grazing bifurcation that defines the onset of chattering motion is thus analysed as are secondary (period-doubling etc.) bifurcations of chattering orbits, and convergence of the bifurcation diagrams is established in the vanishing limit of the smoothing parameters. The bifurcation diagrams of the smoothed system are then compared with initial value simulations of the full non-smooth delay differential algebraic equation. These simulations mostly validate the smoothing technique and show in detail how chaotic chattering dynamics emerge from the non-smooth bifurcations of periodic orbits.