Article

Article title SELF-ORGANIZATION OF THE MOTION OF THE MECHANICAL SYSTEM THAT INTERACTS WITH PROCESSING PROCESS
Authors V.L. Zakovorotny, A.D. Lukjanov
Section SECTION V. AUTOMATION AND CONTROL
Month, Year 07, 2015 @en
Index UDC 62-52:681.5
DOI
Abstract The problems of nonlinear dynamics processing materials cutting are represented. The mathematical model of dynamic system with the dynamic link, formed by the cutting process, is proposed. The following features of dynamic link were taken into account: the dependence of the cutting forces from the area of the shear layer; forces lagging with respect to elastic deformation displacement of the tool relative to the work piece; restriction, which applies to the tool movement in rapprochement of the rear tool face and the treated part of the work piece; dependence of forces on the cutting speed. Dynamic subsystem of tool represented as a linear dynamic system in the plane normal to the cutting surface. The proposed model of a dynamic system is a vector model and contains two oscillators, two self-excitation sources and allows for nonlinear dissipation. The general laws of loss of stability of the equilibrium of the system are considered. It was found that because of the uniqueness of the solution of the equation of statics of the system the branching of points balance is not observed in the case of varying the control. Main attention is paid to the analysis of formed attracting sets (orbital asymptotically stable limit cycles, two-dimensional invariant tori and chaotic attractors) in the vicinity of the equilibrium point. The data on the bifurcation of the system in the parameter space and the space of the control parameters as cut of the bifurcation space by planes (α1 , ρ0) and (ρ0 , T). The change in orientation of the oscillation ellipse in a plane normal to the cutting surface were fixed. Transitions from two-frequency process for the single-frequency process and the two-dimensional invariant torus chaotic attractor were shown. The above method of analysis and the results are shared for mechanical systems interacting with different media.

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Keywords Process of cutting; dynamic system; asymptotic stability; invariant manifolds; bifurcation; stability.
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