Nisonger, R., Yen, C., and Antanaitis, D., "High Temperature Brake Cooling - Characterization for Brake System Modeling in Race Track and High Energy Driving Conditions," SAE Int. J. Passeng. Cars – Mech. Syst. 4(1):384-398, 2011, doi:10.4271/2011-01-0566.
At elevated temperatures, such as those encountered under race track or fade test conditions, the closed-form solution to the lumped capacitance model for characterizing brake cooling (fitted to a standard cooling test temperature range) tends to break down and provide an inaccurate representation of brake rotor cooling behavior. Accurate prediction of cooling is fundamental to brake system component sizing and selection of materials at the early stages of a vehicle program; this is especially true of a high performance vehicle with track performance requirements. To this end, alternative approaches to characterizing brake cooling have been examined to determine their suitability for use in measurement and simulation of brake performance.In this paper, three methods of representing in-vehicle measured brake cooling behavior are reviewed and explained (standard temperature range closed-form solution lumped capacitance model, high temperature range closed form solution lumped capacitance model, and numerically solved linearly varying specific heat capacity lumped capacitance model). The efficacy of each model when employed in brake system thermal models is examined via case studies, in which modeled rotor temperatures are compared to in-vehicle measured high energy fade test results. The influence of radial temperature gradients developed in the rotor on cooling behavior representation and on model to vehicle test correlation is also considered.