APPLIED PROBLEMS OF NONLINEAR OSCILLATION AND WAVE THEORY

Self-organization and bifurcations of dynamical metal cutting system

V. L. Zakovorotnyj^a, D. T. Pham^b, V. S. Bykador<sup>a

a</sup> Don State Technical University, Rostov-on-Don
^b Le Quy Don Technical University

Abstract: The problems of nonlinear dynamics of cutting metal are considered in the article. We offer mathematical model of dynamical system that includes a dynamical relation of the cutting process by using turning example. Basic positions of the dynamical relation are the forces dependence of cutting area, the force’s delay of elastic deformation shift of a tool by relative to workpiece, limitations of the cutting forces on clearance face of the tool, dependence of the cutting forces of the cutting velocity. Dynamical subsystem of the tool is described as linear system on perpendicular plane to cutting surface. The principal focus in the paper was given to analyse of forming of attractors near to fixed point (orbitally stable solutions, double invariant toruses). The article provides data about bifurcation of attractors. Design recommendations for the systems that have required attractors in the state space are also given at the paper.

Keywords: Dynamical system, attractors, bifurcations, cutting process of the materials, Dynamical system, attractors, bifurcations, cutting process of the materials.

UDC: 621.91: 531.3

Received: 18.03.2014