APPLIED PROBLEMS OF NONLINEAR OSCILLATION AND WAVE THEORY

Influence of a flexural deformation of a tool on 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: In the article we offer to consider case of a flexural deformation shifts of a tool when they are essential for nonlinear dynamics of cutting process. This situation is observed for drill deep holes, because a boring bar has a small values of a flexural stiffness. In that case an angle of cutting edge reduces and cutting forces increase if the deformation shifts also increased in velocity direction. The last circumstance becomes occasion for positive feedback that essentially changes dynamics of the cutting process. In the paper it is shown that process with positive feedback has the bifurcation. In the first place we can observe bifurcation of fixed points. In the second place we can watch if stiffness of cutting process is increased that limit cycles and chaotic attractors with limit region of attract are generated in neighborhood of fixed points. It is shown that attracting sets fundamentally depend on cutting parameters. The cutting parameters define cutting forces and the flexural deformation shifts of a tool.

Keywords: Dynamical system, attracting sets, chaotic attractor, bifurcations, cutting process of the materials.

UDC: 621.91: 531.3

Received: 18.03.2014