A scaled axisymmetric finite element model for heat flow in ventilated brake rotors

Abstract

The aim of this thesis was to develop a finite element model of the heat flow in a ventilated disc brake that is both accurate and computationally efficient. The model is intended to be used during the early stages of development for brake components. It must capture the out-of-plane effects on the non-axisymmetric ventilation layer while remaining two dimensional to allow for fast simulations. To accomplish this an enriched two-dimensional model was developed where each edge and face are scaled based on their size in the out of plane direction. The scaling factor was acquired by doing a geometry mapping of each surface and volume on a three-dimensional model of the brake disc, using it to integrate the weak-form over the out of plane dimension. The scaled axisymmetric model was validated against the result of a high-fidelity three-dimensional model of the brake disc supplied by Volvo Car Corporation. The difference between the simulation result of the scaled two-dimensional axisymmetric model and the three-dimensional model was only about 1% when considering heating of an insulated wheel. When adding boundary condition pertinent to the convection over all surfaces, the difference in simulation results becomes about 5%. In both simulation cases, the scaled two-dimensional axisymmetric model accurately captures the average temperature distribution of the three-dimensional model. This accuracy is good considering the difference in computational cost between the models. The scaled two-dimensional model takes minutes to compute while the three-dimensional model takes several hours, which is a good trade off during the early development stages of a brake rotor.