Abstract

To study the technological process of rolling solid and hollow round profiles, it is important to have a correct mathematical description of the patterns that determine the boundaries of the deformation zone. The article analyzed scientific works that examine the calculation of geometric parameters of the deformation zone during the rolling of solid and hollow round profiles in two-roll and multi-roll calibers. As a result of the analysis, a conclusion was drawn regarding the necessity of a more detailed description of the determination patterns for the geometric boundary conditions of the deformation zone. This led to the proposal of a universal method for determining the shape of the billet and the shape of the caliber groove, as well as the derivation of the equations for the roll surface and the boundary of the contact surface of the deformation zone for various rolling schemes. The developed method allows for an increase in the accuracy of calculating the energy-force parameters of the rolling processes, including continuous rolling, in the production of solid and hollow round profiles according to the circular–oval scheme in calibers formed by any number of rolls, thanks to the consideration of a sufficiently wide range of geometric features

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