Mathematical models of temperature in electric discharge rolling of metals

Abstract

The model of analytical calculation of the average volumetric temperature of plastic deformation in the conditions of applied impulse current was developed on the base of rolling energy balance. Additionally, the formula for determination of the contact temperature between rolls and strip as well as temperature gradient through strip thickness and its variation in time of electroplastic process conduction was concluded on the base of solution of the heat conductivity differential equation in Fourier partial derivatives. This equation is valid for the boundary condition taking into account joint heating with impulse current and plastic deformation. Conducted temperature calculations for dimensionless time in the deformation area during electric discharge rolling of steel 3 and VT-6 titanium alloy displayed that temperature rise up to its maximal value has temporal displacement to strip exit side of deformation area. It is connected with temporal retarding of heat forming comparing with the time of elastic-plastic deformation. As soon as the contact square of rolls with strip has two different areas, where bonding and slipping are realized via rolling friction and slipping friction, immediate temperatures will also differ respectively. The obtained models allow to conduct calculations of the contact temperatures in the areas of roll bonding and slipping relating to the rolling strip. Electric discharge rolling reduces conventional cold rolling technology via elimination of heating with intermediate heat treatment (annealing) and improves thereby thin strip quality via healing of its cracks and defects by electric impulses, as well as increases productivity by 30 %.