Abstract

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.

中文翻译：

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压缩空气对铁路轨线差异化热处理的模拟

摘要

已经对空气与空气进行差异化热处理的数学模型进行了建模。在第一阶段，通过解析和数值方法解决了具有第三类边界条件的一维导热问题。将在轨头表面和距滚动表面20毫米深度处获得的温度分布与实验数据进行比较。结果，确定了轨道钢的传热系数和导热系数。在第二阶段，在强制冷却以及随后自然对流冷却的条件下，创建了钢轨模板中温度分布的数学模型。所提出的数学模型基于Navier–Stokes和淬火介质的对流热导率方程以及钢轨的热导率方程。在轨道-空气边界上，设置了热流连续性的条件。在自然冷却的条件下，利用第三种条件下的热传导方程模拟了温度场的变化。一维热传导方程的解析解表明，计算出的温度值与实验数据相差10％。当冷却持续时间超过30 s时，温度随时间变化的曲线就会发生变化，这与冷却机制的变化有关。数值分析的结果证实了这一假设。通过有限元方法对钢轨冷却的二维模型进行分析，结果表明，钢轨头部的表面温度在初始冷却阶段沿中心轴和圆角都急剧下降。当冷却时间超过100 s时，温度稳定在307K。在轨头的中央区域，冷却过程比在表面区域慢。停止强制冷却后，由于从中心区域到导轨头表面的热流方向发生了变化，因此观察到了表面层的加热，然后以明显低于第一阶段的速度进行冷却。获得的结果可用于校正差异硬化模式。