One-Dimensional Thermal Model and Temperature Estimation for a MotoGP Class Motorcycle Carbon Brake

Abstract

In the past few decades, braking systems with carbon discs have become the dominant technology for many racing applications, such as in the MotoGP class. Indeed, they provide higher friction coefficients and, thanks to their lightweight materials (with respect to conventional steel brakes), the unsprung masses and the gyroscopic effects can be reduced, thus improving the motorcycle dynamic performance. However, carbon brakes can work properly only within a relatively narrow operating temperature range. Hence, an accurate assessment of their actual thermal behavior is mandatory. After a brief introduction to Bayesian inference theory, this paper focuses on the development of the Unscented Kalman Filter (UKF) algorithm as a suitable mathematical tool for assessing the temperature gradient of the carbon disc. The UKF belongs to a category of optimal estimation algorithms (called Bayesian recursive filters) that use both the sensor measurement and a physical model to calculate the optimal posterior estimate for the state of the system. This paper will go through the simplified one-dimensional finite element model representative of the thermodynamics of the brake that is employed by the UKF for the posterior optimal temperature estimation. Finally, an unconventional usage of the UKF is proposed which turned out to be particularly effective for the identification of the parameters in the thermal model that cannot be directly measured.