Applicability of the laws of elasticity for the determination of the elastic-region length in the deformation zone during cold rolling

The errors of calculating the energy-force parameters of cold rolling are analyzed. They appear because of the assumption of the classic rolling theory about the applicability of the Hertz formula, which is known in the theory of elasticity, to the calculation of the elastic-region length in the deformation zone. The Hertz formula, which is used to calculate the half-width of the contact area between a fixed cylinder and a plane that bounds an elastic half-space, is shown not to take into account the following factors that are characteristic and important for the roll-strip contact: the cold working of the strip, the strip thickness, the rotation of rolls accompanied by sliding friction, and the wear that decreases the initial roll roughness (i.e., changes in the friction coefficient). A method is proposed for taking into account these factors in the calculation of the energy-force parameters of cold rolling; it is based on the statistical processing of the parameters that are measured in operating mills and are present in the databases of their process control systems. The application of this method decreases the errors of calculating the rolling forces by 35–40% and refines some laws of the state of stress in a rolled strip.