Chaotic vibrations in high-speed milling

A large number of literatures are devoted to the stability of the milling process and various control methods for chatter suppression. But chaotic dynamics beyond the stable region has not been considered extensively. Moreover, modeling issues for chaotic motion need more challenge for accurate prediction of its complex dynamical behavior. This paper presents a detailed two-degree-of-freedom mechanics based model for the study of chaotic vibrations in milling. Segmental multiple regenerative effect that is the principle feature of nonlinear vibrations in milling processes besides two state dependent time delays has been considered. Exact geometrical formulation of multiple regenerative effects by considering simultaneously different numbers of delayed tool positions over the cutting zone is presented for the first time. Phase portrait, bifurcation diagram, largest Lyapunov exponent, and surface profile were calculated for a given machine tool and workpiece parameters. The simulation results show positive values of the largest Lyapunov exponent corresponding to the existence of chaos in high-speed milling operations. Also, investigation of the machined surface of the workpiece formed by the helical mill demonstrates an irregular pattern on the surface.