Calabrese, F., Baecker, M., Galbally, C., and Gallrein, A., "A Detailed Thermo-Mechanical Tire Model for Advanced Handling Applications," SAE Int. J. Passeng. Cars - Mech. Syst. 8(2):501-511, 2015, doi:10.4271/2015-01-0655.
Currently used tire models have shown a certain lack of accuracy in some advanced handling applications. This lack of accuracy is believed to be partly due to thermal effects. In reality, the tire rubber temperature is not constant during the normal operating conditions and it's really well known that the tire friction coefficient strongly depends on the temperature level.The temperature generation, propagation and evolution are the result of a dynamic energy equilibrium between phenomena of different natures. Various mechanisms create a non-uniform temperature distribution in various parts of the tire structure: heat is generated in zones with large cyclic deformations due to the energy dissipated from the rubber strains and in the sliding part of the contact patch due to friction. The rubber cools down because the heat energy transferred to the air (internally and externally) and to the asphalt in the stick zone of the contact patch. The presented thermodynamic tire model allows for the simulation of all these local thermal phenomena and the thermal energy equilibrium is described by the Fourier diffusion equation solved with a finite volume approach.Furthermore the described thermal model is coupled with the structural MBD tire model ‘CDTire/3D’ and with an enhanced magic formula (MF) formulation. The coupling strategy naturally incorporates the structural tire model, while in the case of the MF model some empirical adaptations are needed. Both tire models' behavior is influenced by the local calculated temperature, e.g. by modifying the local friction of the tread/asphalt contact. One result the model clearly shows is the variation of the road holding performance as a consequence of the temperature evolution. The capabilities of the overall model are demonstrated and validated in some illustrative scenarios by using measured date from motorsport applications.