ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Zakovorotny V. L., Pham D. T., Bykador V. S. Self-organization and bifurcations of dynamical metal cutting system. Izvestiya VUZ. Applied Nonlinear Dynamics, 2014, vol. 22, iss. 3, pp. 26-39. DOI: 10.18500/0869-6632-2014-22-3-26-39

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
621.91: 531.3
DOI: 
10.18500/0869-6632-2014-22-3-26-39

Self-organization and bifurcations of dynamical metal cutting system

Autors: 
Zakovorotny Vilor Lavrentevich, Don State Technical University
Pham Dinh Tung, Le Kui Don State Technical University of Vietnam
Bykador Vitalij Sergeevich, Don State 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.

Key words: 
dynamical system
attractors
bifurcations
cutting process of the materials
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Received: 
18.03.2014
Accepted: 
05.05.2014
Published: 
31.10.2014
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