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

Abstract

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.

Research on Influence of Tool Deformation in the Direction of Cutting and Feeding on the Stabilization of Vibration Activity during Metal Processing Using Metal-Cutting Machines

“…The F c component has the greatest value here, which most accurately reflects the cutting force itself, and determines the vibration activity of the tool in the direction of the z axis. The force itself, which prevents the shaping movements of the tool, can be represented as the product of the cut layer area by some indicator characterizing the chip pressure on the front face of the cutting wedge of the tool, as presented in the expression below [20][21][22][23][24][25]:…”

“…As for the amount of feed per revolution, this will be determined as the solution of the following integral [20][21][22][23][24][25]:…”

“…When forming the feed, two arrays of trajectories are considered, which are shifted relative to each other in time via a constant value of the lagging argument. As a result, the effects of synchronization and asynchronous interactions, as well as the effects of complex formation, attracting sets of feeds, and corresponding cutting forces, are observed, which can lead to the formation of chaotic attractors of deformations [22][23][24][25]. In addition to the regeneration of vibrations during cutting, the dynamics of deformation movements of the tool tip are also significantly affected by the process of temperature formation in the contact zone of the tool and the workpiece, which includes the conversion of irreversible transformation power into heat generated during cutting [26].…”

“…The declared approaches to the formation of mathematical models of cutting control systems [20][21][22][23][24][25][26] are largely based on the representation of forces that hinder the formative movements of the tool in the coordinates of deformations of the tool tip. With this representation, the lag constant, in the real cutting process determined by the spindle revolution speed and the deformation mixing of the tool tire in the cutting direction, should also be represented in the same coordinates.…”