Mathematical modeling of vibration resistance of long turning of slender parts

This paper is devoted to mathematical modeling of vibration-resistant machining of low-rigidity parts. The relevance of this research stems from the occurrence of significant vibrations in the workpiece during machining on a metal-cutting machine. The vibrational process can be so intense that it necessitates a significant reduction in the cutting mode when machining such parts, resorting to multi-pass machining, and increasing the number of the piece repositioning in the machine tool fixtures. This process also increases cutting tool wear, which ultimately leads to a decrease in the productivity of machining such parts on machine tools. The objective of this research is to develop mathematical cutting models that take into account complex dynamic processes occurring during metal cutting. The proposed method for dissecting the dynamic cutting characteristic into two basic characteristics makes it possible to construct mathematical models that take into account the complexity and diversity of the phenomena arising during fast-moving dynamic processes. The paper substantiates the fundamental theoretical principles for constructing a generalized model focused on the process of constrained oblique cutting of a machine tool’s dynamic system. Dynamic cutting characteristics of the first and second kind were obtained experimentally for straight-turning tools with different geometries.