Koinov T.Bel’Skii S.M.Mukhin Y.A.Chuprov V.B.2024-07-142024-07-142024-07-142024-07-142018-01-012410-20910368-079710.17073/0368-0797-2018-5-348-356SCOPUS_ID:85048764929https://rlib.uctm.edu/handle/123456789/982Based on the Jourdain variation principle, a mathematical model of the process of free widening in hot rolling of thin sheet metal is developed. The principle applies to rigid-plastic materials and for the cinematically admissible area of speeds. As a functional of the variational equation, sum of the powers of internal resistances, frictional forces, shear forces, front and back tension was used. When solving the Jourdain variational equation for the case of rolling with tension, the Ritz method was applied. The Jourdain variational equation was transformed into a system of homogeneous equations, the left side of each represented a derivative with respect to a varying parameter. Varying parameters were the exponent of the kinematic condition, general widening in the plastic deformation zone and the widening in its neutral section. The developed model allows to study the distribution of the widening on length of the deformation zone depending on the parameters of rolling process and sheet metal. To test the adequacy of the developed free-widening model, experimental studies were carried out on a two-roll cold rolling mill. Lead samples were rolled, the measured widening values of which coincided with the theoretical calculated with an accuracy of less than 10%. Cold rolling of lead samples simulates hot rolling. Theoretical analysis of the influence of tension on the process of free widening when applying tension is consistent with the practical results presented in the literature. It is shown that the unevenness of tensile stresses in the input and output sections of the deformation zone arising from the application of tension causes the appearance of additional powers in the power balance equation, leading to a decrease in magnitude of the widening. The resulting unevenness of the tensile stresses can be used to control magnitude of the widening in thin-sheet rolling. In turn, unevenness of the tensile stresses along the width of rolled strip can be increased or decreased by means of the bending forces of work rolls of the rolling stand. The article presents a scheme for controlling the value of the rolling band widening during hot rolling with the help of bending forces of work rolls.enArticle