Explanation of random vibrations in cutting on grounds of deterministic chaos

Abstract This article presents a model of orthogonal cutting on an elastic system. The dynamics of the system is described by the differential equations in which the forces are expressed by empirical nonlinear relations. The oscillations of the system determined by numerical solutions of nonlinear differential equations exhibit chaotic characters in certain domains of typical parameters and thus represent a new example of deterministic chaos. This indicates that, besides the irregular properties of cut material, nonlinear dynamics must also be taken into account in order to explain the random character of vibrations observed in cutting systems.