Estimation of temperature distribution in brake shoes is very important in order to prevent thermal damages such as cracks, fading etc. In this research, the thermal model of brake shoe in a train is introduced considering time-dependent frictional heat load in two modes of emergency and continuous braking. The governing heat conduction equation is solved in polar coordinate by using the method of separation of variables combined with Duhamel integral and a closed-form solution is introduced. Results show the good ability of analytical solution to estimate exact temperature profile in composite and cast iron brake shoes. The ability of the solution for estimation of braking situation to prevent from melting criteria is demonstrated. The composite brake shoe will reach to the melting point of 590 °C in continuous braking at the speed of about 120 km/h and the fading limit in cast iron shoe is occurred after 8 sec in emergency braking mode. The introduced thermal model can be applied as a verification branch of other works and can reduced the huge costs of experimental tests of brake shoes.

估计闸瓦内的温度分布对于防止裂纹、褪色等热损伤非常重要。 本研究引入列车闸瓦热模型，考虑两种紧急情况下的瞬态摩擦热负荷和连续制动。采用分离变量法结合Duhamel积分法在极坐标下求解控制热传导方程，并引入了闭式解法。结果表明解析解能够很好地估计复合材料和铸铁制动蹄中的精确温度分布。证明了估计制动情况的解决方案防止熔化标准的能力。复合制动蹄在120km/h左右的速度连续制动时会达到590°C的熔点，在紧急制动模式下8秒后出现铸铁蹄的褪色极限。引入的热模型可以作为其他工作的验证分支，可以降低制动蹄实验测试的巨大成本。