Simulation of Differentiated Thermal Processing of Railway Rails by Compressed Air

Mathematical modeling of differentiated thermal processing of railway rails with air has been carried out. At the first stage, the one-dimensional heat conduction problem with boundary conditions of the third kind was solved analytically and numerically. The obtained temperature distributions at the rail head surface and at a depth of 20 mm from the rolling surface were compared with experimental data. As a result, the coefficient values of heat transfer and thermal conductivity of rail steel were determined. At the second stage, the mathematical model of temperature distribution in a rail template was created in conditions of forced cooling and subsequent cooling under natural convection. The proposed mathematical model is based on the Navier–Stokes and convective thermal conductivity equations for the quenching medium and thermal conductivity equation for rail steel. On the rail–air boundary, the condition of heat flow continuity was set. In conditions of spontaneous cooling, change in the temperature field was simulated by a heat conduction equation with conditions of the third kind. Analytical solution of a one-dimensional heat conduction equation has shown that calculated temperature values differ from the experimental data by 10%. When cooling duration is more than 30 s, the change of pace of temperature versus time curves occurs, which is associated with change in cooling mechanisms. Results of numerical analysis confirm this assumption. Analysis of the two-dimensional model of rail cooling by the finite element method has shown that surface temperature of the rail head decreases sharply both along the central axis and along the fillet at the initial cooling stage. When cooling duration is over 100 s, temperature stabilizes to 307 K. In the central zones of the rail head, the cooling process is slower than in the surface ones. After forced cooling is stopped, heating of the surface layers is observed, due to change in heat flow direction from the central zones to the surface of the rail head, and then cooling occurs at speeds significantly lower than at the first stage. The obtained results can be used to correct differential hardening modes.