Analytical model of the steady state temperature distribution in a single and multi-layer brake disc

Abstract

This article focuses on the modeling and analyzing effort for the thermal analysis and design of disc brake for endurance braking scenario. Test cases of bike disc brake rotor are chosen as its unique double layered architecture has been recently proposed for thermal optimization especially. This work aims at the evaluation of the steady state temperature distribution during braking to be studied considering a constant rotation speed and localized heat sources at the brake pad area. The problem is solved analytically using variable separation and a double Fourier - Hankel transforms.The modelling strategy is developed for a single layered rotor as reference cases for various rotation speed and rotor thicknesses. The effect of the rotation speed is underlined using a representative constant heat exchange coefficient. For high rotation speed (greater than 50 rad s-1 for the studied geometry), an effective surface layer can be observed which limits the influence of the rotor thickness on the temperature level. The model is extended to a multi-layered material rotor architecture. The potential advantages of this composite structure for different layer thicknesses and materials are evaluated and discussed. It appears that the aluminium core provides the better results, yet the relative reduction of the temperature compared to a plain stainless steel disc is of about 1 % only.