Abstract
Mathematical modeling of differentiated thermal processing of railway rails with air has been carried out. At the first stage, onedimensional heat conduction problem with boundary conditions of the third kind was solved analytically and numerically. The obtained temperature distributions at the surface of the rail head and at a depth of 20 mm from the rolling surface were compared with experimental data. As a result, value of the coefficients of heat transfer and thermal conductivity of rail steel was determined. At the second stage, 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, condition of heat flow continuity was set. In conditions of spontaneous cooling, change in temperature field was simulated by heat conduction equation with conditions of the third kind. Analytical solution of 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, 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 at the initial stage of cooling, surface temperature of the rail head decreases sharply both along the central axis and along the fillet. When cooling duration is over 100 s, temperature stabilizes to 307 K. In the central zones of the rail head, 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.
Highlights
When cooling duration is more than 30 s
Сарычев В.Д., Хаимзон Б.Б., Невский С.А., Ильященко А.В., Гришунин В.А
Summary
Анализ двухмерной модели охлаждения рельса методом конечных элементов показал, что на начальном этапе охлаждения температура поверхности головки рельсов как по центральной оси, так и по выкружке резко уменьшается. После прекращения принудительного охлаждения наблюдается нагрев поверхностных слоев, обусловленный сменой направления теплового потока от центральных областей к поверхности головки рельса, а затем происходит охлаждение со скоростями существенно меньшими, чем на первом этапе. В настоящее время большинство современных отечественных рельсов изготовлены с применением технологии дифференцированной закалки воздухом с использованием остаточного тепла предпрокатного нагрева, так как она обладает лучшей контролируе мостью и большей экологичностью [5]. Поиск оптимальных режимов термической обработки, обеспечивающих высокие механические свойства рельсов, является сложной задачей, решение которой требует применения не только экспериментальных методов, но и математического моделирования [10, 11]. Целью настоящей работы является разработка механизма и математической модели, которая с достаточной точностью описывает процесс управляемого охлаждения рельсов
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