The influence of sections of the elastic deformation of a strip on the length of the deformation zone during cold rolling

A numerical analysis method was developed for a stress-strain state stock material at the elastic strain deformation zone during cold rolling. Considering the deformation of rolls, the stock material was divided into finite volumes, where the system of equations for relationships of stresses and deformations of the theory of elasticity and the equations of equilibrium were analytically solved. A size of the elastic and plastic sections and the contact stresses at their boundaries were determined. Was established that ultimate strain at the elastic zone of a strip recovery and contact stresses at the border between elastic and plastic zones at the exit from deformation zone increases at decreasing strip compression and increasing friction ratio. A boundary condition was found, in cases of exceeding that condition it comes to significantly increasing arc of contact length and rolling force. In a case when the elastic strip deformation does not reach this boundary condition, the elastic strip deformation does not impact significantly at the rolling force. According to the presented method considering an elastic strip deformation while s=0.05 lead to increasing arc of contact length and rolling force at 10–17%, at implementation in a practice rolling cases. An inaccuracy of using known methods was estimated.