Abstract
Abstract Thermo-mechanical phenomena that occur during the metals cutting in a cylindrical form are difficult in terms of systematic and interconnected mathematical description for a three-dimensional deformable body. In this connection, empirical formulas of the cutter interaction with the processed surface of metal products are used in calculations. In this paper, we propose the most general approach for modeling the process of metalworking by thermodynamically nonlinear strain. Using the non-classical theory of deformation, the three-dimensional problem of metalworking by cutting is reduced to a two-dimensional one. The proposed approach made it possible to compose resolving equations and boundary conditions for the problem under consideration, taking into account heat release and wear on contact sur faces with a cutting tool.