چكيده به لاتين
Abstract
The issue of heat transfer in the brakes of trains and wheels of railway vehicles is one of the important issues that should be considered in order to save time, cost and improve the performance of the brake system, and ignoring it may cause malfunctions in the brake system and extreme damage to life and property. The braking phenomenon is accompined by an increase in temperature and heat production, which must be controlled in some way. The heat generated causes initiation and growth of temperature cracks, which grow over time and eventually fail. One of the systems used in freight and passenger train brakes is shoe brakes.
This study deals with the mathematical modeling of the distribution of shoe temperature and train wheel during braking. In this analytical solution, the shoe is assumed to be a piece of a hollow cylinder with a frictional heat from the contact with the wheel on the inner surface, but the outer surface and its side surfaces have a boundary condition of convection heat transfer with the ambient air. In this solution, the wheel is also assumed to be a hollow ring, on the outer surface of which the heat of moderate friction caused by contact with shoe is considered, and the inner surface has the boundary condition of convection heat transfer with ambient air.
For analytical solution of heat transfer equations in shoe and wheel, the method of separation of variables in the polar coordinate system has been used and the shoe is designed as a two-dimensional piece and the wheel is in one-dimensional (symmetrical axial) mode. This solution consists of three parts: 1- Solving the steady-state equation 2- Solving the transient-state equation 3- Get the Duhamel integral from the temporal part of the answer and get the closed-form solution.
Then, the answer of the problem is plotted by coding in MATLAB software for two types of cast iron and composite brake shoes and steel wheel in two modes of continuous and emergency braking and is compered with the test results obtained from previous studies.
Keywords: Brake shoe; Train wheel; Analytical solution; Polar coordinate
