The Properties of Attracting Sets of Tool Deformation Displacements in the Trajectories of the Shape-Generating Movements in Turning

To date, there are many models of cutting forces as a function of deformations determining the dynamic relationship of the cutting process, which are based on experimental data, for example, on phase shifts between deformations and forces. However, a systematic study of the dynamic cutting system properties and the attracting sets of tool deformation displacements has not been carried out. The article considers system properties of the attracting set formation and proposes directions allowing their controlling. The cutting forces depending on deformations that form an intra system feedback, which can stabilize the equilibrium as well as contribute to the loss of its stability, were studied. The main results were obtained by mathematical modeling, and the methods of experimental dynamics were also used. Based on the results of the study, the conditions for self-excitation of the dynamic cutting system depending on the deformations in the direction of the cutting speed were determined. The obtained data on the mechanisms of formation and evolution of the attracting sets of tool deformation displacements during cutting allowed finding a new direction for increasing the cutting efficiency based on a constructive change in the elastic properties of the tool subsystem, its geometry and matching the CNC program with the dynamic properties of the cutting process.

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