Rolling of rail profiles in a universal groove. Part 1

A mathematical model of the shaping of metal on rail rolling in universal grooves is developed by variation so as to minimize the total power consumption, using up-to-date computer resources. This model permits uniform deformation of all elements of the rail profile. In particular, a geometric model of the deformation region is formulated, and the kinematically possible flow-rate field for the metal is established. The boundary conditions are determined, and the basic system of equations is derived, including the energy-balance equation and the condition for a minimum of the variational functional. In contrast to familiar variational solutions, all the equations in the mathematical model are calculated without simplifications. That increases the accuracy of the calculation. The proposed model may be used to determine the metal flow for rolling in universal grooves. © 2015, Allerton Press, Inc.