Building a Mathematical Model for Elastic–Thermodynamic Interaction Occurring in the Process of Cutting on a Lathe Machine, Taking into Account Nonlinear Friction

This article studies the problem of modeling the nonlinear characteristics of friction using digital twins for cutting process on metal-cutting machine tools. One of the important characteristics of a mathematical model for the cutting force response to the shaping movements of a cutting tool is the friction coefficient between a cutting tool’s flank wear land and the machined workpiece surface. The dependence of the friction coefficient on the temperature–velocity parameters during cutting is widely known, whereas the mathematical dependences within the general mathematical model for elastic–thermodynamic interaction during cutting have not been determined yet. Therefore, the aim of this study was to create a mathematical model that would reveal the dependence of the friction coefficient between the cutting tool’s flank and the machined workpiece on the temperature of this interaction. To create a model, the authors relied on both the analysis of theoretical studies and the results of a full-scale experiment conducted to determine the actual value of the friction coefficient. By achieving the aim of this study, the authors have refined the general mathematical model for elastic–thermodynamic interaction occurring in the process of cutting on a lathe by taking into account the adhesion–diffusion nature of friction in the contact zone of the cutting tool’s flank and the machined workpiece. Furthermore, the general mathematical model has been validated based on the data obtained in a series of additional experiments using the modern STD.201.1 measuring bench.