Application of the variation principle for calculating the force-energy parameters of rail rolling by a universal mill

In order to simplify the three-dimensional geometrical model of rail rolling by a universal mill, the vertical roll with box pass was simplified as an equivalent flat roll firstly. Then the kinematically admissible velocity fields of the web, head and base of a rail were determined. Based on these velocity fields, the plastic deformation power, the powers consumed on the velocity discontinuity surface and the powers generated for backward slip and forward slip were calculated. According to the variation principle, the roll forces of a horizontal roll and two vertical rolls were obtained. Compared with experimental data, the values of roll force from the upper-bound method are somewhat greater than experimental data but do not exceed them by 20% in general. The method with the variation principle is reliable and feasible to preset and optimize the parameters of rolling technology.