The work objective is to study the formation of orbitally asymptoti-cally stable limit cycles and two-dimensional invariant tori includ-ing bifurcations near the attracting sets. The investigators use pri-marily methods based on the mathematic simulation of the dynamic systems. Some problems of the nonlinear dynamics of the material cutting are considered. A mathematical model of the dynamic sys-tem considering the dynamic link formed by the cutting process is offered. Here, the following key features of the dynamic coupling are taken into account: dependence of the cutting forces on the area of a cut-off layer, delay of forces towards the elastic deformation shifts of the tool in relation to the workpiece, restrictions imposed on the tool movements when the back of the instrument is ap-proaching the treated part of the workpiece, forces – cutting veloci-ty relation. The dynamic subsystem of the tool is presented by a linear dynamic system in the plane orthogonal to a cutting surface. Following the research, some guidelines for designing systems with the required stationary manifold in the state space are provid-ed. Importantly, in the neighborhood of equilibrium, various crite-ria of set causing regular or irregular features of the formed in-cut surface can develop depending on the models interacting under processing.
materials cutting, dynamic system, invariant manifold, bifurcations
Введение. Проблемы динамики процесса резания исследуются в течение последних 50 лет. При этом внимание уделялось, главным образом, двум вопросам: условиям и механизмам возбуждения автоколебаний [1–5] и анализу устойчивости процесса резания [6–10]. Довольно активно изучаются подсистемы инструмента и обрабатываемой заготовки, их взаимодействия через динамическую связь, формируемую процессом резания. Полученные в результате данные служат основой для исследования динамики процесса резания.
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