The hardening-finishing treatment of parts surface with rolling by steel cylindrical rollers produces low roughness, reduced residual compression stresses, and fine-grained structure due to plastic deformations. The deformation of metals during machining at high temperatures is characterized by a significant influence of strain rates on stresses. This necessitates the calculation of stresses and strains based on the equation of state of rheonic bodies. This study aims to determine the components of stresses and force factors of the technological process of finishing and strengthening machining of the surface of parts by deriving the analytical solutions to calculate the stress- strain state within the deformation zone based on creep theory. In this problem, general formulas are obtained for calculating the stress-strain state, pressure and friction forces on the contact surface, as well as forces and moments acting on the roller. Numerical analysis using Mathcad explores the understanding of the stress-strain state in the deformation zone on the force factors of the technological process. The obtained results are beneficial for establishing the mode of thermomechanical processing and selecting appropriate technological equipment for restoring flat surface parts.
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