Flexural Forces of the Working Rollers and the Broadening of Thin Steel Strip in Hot Rolling

Abstract

On the basis of the Jourdain variational principle for a rigid–plastic body and the kinematically permissible velocity field, a model of the free expansion in the hot rolling of thin sheet is developed. The functional used in the variational equation is the total power of the internal resistances, the slipping-friction forces, the shear forces, and the front and rear tension. The Ritz method is used in solving the Jourdain variational equation for rolling with tension. The Jourdain variational equation is converted to a system of uniform equations, with a derivative of a variable parameter on the left side of each. The variable parameters are the exponent of the kinematic condition; the total broadening in the plastic-deformation region; and the expansion in its neutral cross section. The mathematical model developed for the broadening of hot-rolled strip may be used to investigate the distribution of broadening along the plastic-deformation region as a function of the parameters of the rolling process and the strip. To verify the model of free expansion, experiments are conducted on a two-roller laboratory cold-rolling mill. Lead samples are rolled. Their measured broadening matches the theoretical values to within 10%. The cold rolling of lead samples simulates hot rolling. Theoretical analysis of the influence of tension on the free expansion is consistent with practical results in the literature. The nonuniform tensile stress seen in the input and output cross sections of the deformation region when tension is applied gives rise to additional powers in the balance equation, with consequent decrease in the broadening. The resulting nonuniformity of the tensile stress may be used to regulate the broadening in thin-sheet rolling. In turn, the nonuniformity of the tensile stress over the strip width may be increased or decreased by means of the flexural forces of the working rollers in the mill. A method of regulating the broadening of the strip in hot rolling by means of the flexural forces of the working rollers is outlined in the present work.