Three-dimensional analytical calculation of the temperature in a brake disc of a high-speed train

Abstract

In this paper, an analytical model is developed to determine the 3D temperature distribution in a brake disc of a high-speed train. In this system, the brake pad is composed from multiple pins. In order to solve the heat transfer problem, the Fourier and Hankel integral transforms are used to perform the analytical calculations. The expression obtained by this way is explicit and allows one to compute the temperature distribution in the disc whatever the rotating speed, the number and the size of the spots, and the physical properties values. A compensation term due to the fact that the surface of the spots is not negligible compared to the surface of the disc is introducing in the model. Indeed, the fact that the analytical model assumes a convection term on the friction surfaces, which is not the case, must be fixed. Then, the analytical model is validated by comparing the results with those of a numerical simulation.