WSEAS Transactions on Applied and Theoretical Mechanics
Print ISSN: 1991-8747, E-ISSN: 2224-3429
Volume 10, 2015
Bifurcations in the Dynamic System of the Mechanic Processing in Metal-Cutting Tools
Author: Vilor Zakovorotny
Abstract: The nonlinear dynamics in processing of metal-cutting tools is considered. The author proposes the mathematical model that includes two spatial elastic subsystems. They interact through the dynamic connection, which is a force in the model of coordinates of the system state. The simultaneous excitation sources and nonlinear damping vibrations of the cutting tool are taken into consideration in the model. This approach allows defining the following system properties: branching equilibrium points; the conditions under which generated limit cycles and invariant tori; the formation of chaotic dynamics. The dynamic subsystem tool is presented as the linear dynamical system in the normal plane. The main attention is paid to the analysis of bifurcations in the space of parameters of dynamic equations, as well as in the space of control parameters. General patterns of loss of stability of equilibrium of the system are considered. The role of acceleration of gyroscopic and circulation forces is specified. The results are important for the analysis of motion of mechanical systems that interact with various environments (processes of friction, hydrodynamic, aerodynamic, etc.).
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Keywords: processing, metal cutting, dynamic system, asymptotic stability, invariant manifolds, bifurcation
Pages: 102-116
WSEAS Transactions on Applied and Theoretical Mechanics, ISSN / E-ISSN: 1991-8747 / 2224-3429, Volume 10, 2015, Art. #11