Relationship between the Frequency of Development of Shear Displacements of Metal and the Size Factor of the Deformation Site during Longitudinal Rolling of Blanks

Using the technique applied in the analysis of vortex fields, shear displacements of metal along the trajectory of a logarithmic spiral during longitudinal rolling of blanks were investigated. Knowledge of the regularity of the development of the shear trajectory made it possible to establish the radii of the trajectories of shear displacements of metal when modeling the process of rolling blanks in rolls with a diameter of 1200, 1000, and 800 mm and to establish the frequency of development of shear displacements of metal for the rolls of the studied series. The results were obtained for the ratios of the thicknesses of the lamellas (strips) δ₃/δ₁ formed during shear, or the frequency of development of shear displacements of the metal in the form of the following ratios: δ₃/δ₁ = 3.2, δ₃/δ₂ = 1.7, δ₂/δ₁ = 1.8, the numbering order corresponds to the given size series of rolls. The specified values show the level of deformation effect on the metal of the technological tool depending on its dimensions.