Issue 37

U. Muhin et alii, Frattura ed Integrità Strutturale, 37 (2016) 318-324; DOI: 10.3221/IGF-ESIS.37.42 318 Focused on Fracture Mechanics in Central and East Europe Study of the influence between the strength of antibending of working rolls on the widening during hot rolling of thin sheet metal U. Muhin, S. Belskij Lipetsk State Technical University, Lipetsk, Russia , nemistade@mail.ru T. Koynov University of Chemical Technology and Metallurgy , Sofia toni309@koinov.com A BSTRACT . Based on the variation principle of Jourdan was developed a mathematical model of the process of widening freely in hot rolling of thin sheet metal. The principle applies to rigid-plastic materials and for the cinematically admissible area of speeds. The developed model allows to study the distribution of the widening on the length of the deformation zone depending on the parameters of the rolling process and sheet metal. Results are obtained, characterizing the size of the widening and effectiveness of the process control on tension at the entrance and exit from the stand. The widening is dependent on the strength of anti bending. K EYWORDS . Widening; Anti bending; Hot rolling; Thin sheet; Model A THEORETICAL ANALYSIS OF THE PROCESS OF BROADENING or theoretical analysis of sheet rolling, in particular, the process of broadening of the metal in the deformation zone, successfully using the energy method, based on the beginning of the possible changes of the deformed state (beginning of Lagrange). It is a kind of variation principle Jourdain, according to which the variation of the flow velocity of the metal to be in the focus of the plastic deformation. Jourdain's variation equation for the plastic deformation zone is written as follows:           S n i iS i s n v ds v dsv d 1 0 ) (     , (1) where:    0 d v - the speed potential; T and H - the intensity of shear stress and shear rate; n   , v  - the total stress on the surface S with unit outward normal n  and the appropriate movement speed; F