thermoRIDE

thermoRIDE is a physical-analytical tire thermal model developed, currently employed by motorsport and carmaking companies with the aim to:

• predict local tire thermal distribution in order to analyze the effect on vehicle performance
• simulate tire thermal behaviour in real-time and from telemetry data
• evaluate Pacejka MF micro-parameters linked to tire thermodynamics phenomena
• understand and optimize tire behaviour with consequential setting of proper vehicle setup

The model is able to provide temperature local distribution, with particular reference to the deep layers usually not reached by measurement instruments, accounting for the dissipative phenomena induced by cyclic deformations and for the effects due to thermal exchanges with external environment.
Considering the tire as a thermodynamic system, the following heat transfer mechanisms have been taken into account:

heat generation within the rubber compound due to:

• tire-road tangential interaction, known as “FP” (friction power)
• effect of tire cyclic deformation during the rolling, known as “SEL” (strain energy loss)

heat exchange with the external environment due to:

• thermal conduction between the tread and the road
• convection of the surface layer with the outside air
• convection of the inner liner with the inner air

heat conduction between the tire layers due to the temperature gradient

Depending on the complexity and the geometry, the tire structure is discretized by means of a certain number of layers with peculiar physical characteristics. The layers totally reproduce the tire composite matrix structure, identifiable with tread external surface, tread core, tread interface with belt, belt, plies and inner liner, allowing to better understand the thermodynamics of both the entire tire in terms of stiffness variation and the its components as compound optimum thermal range. The developed thermodynamic tire model is based on the use of the diffusion equation of Fourier applied to a three-dimensional x-y-z domain, further detailed as in the following formulation in order to take into account the variation of the thermal parameters along the thickness z and with temperature T.

As concerns the cited heat transfers, friction powers is calculated at the tire/road interface as the product of sliding speed and tangential force, SEL is taken into account by means of an analytical law accounting for wheel rolling frequency, vertical and tangential tire loads, whose parameters are identified through experimental tests carried out deforming cyclically the tire in three directions (radial, longitudinal and lateral). Thermal exchange between tread and asphalt is modelled again by Fourier’s formula, applied in the contact patch (calculated as a function of vertical load, inner pressure and camber and toe angles) considering an equivalent thermal conductivity coefficient referred to tire tread and to road thermal characteristics. Convection with internal and external air are described by Newton’s forced convection equation.

In its latest versions the model has been optimized in matrix structures in order to reduce computational loads, allowing real-time simulations. New features include the cited wear effect, obtained enabling the removal of tread surface layers with a certain wear rate during the simulations, local input management, useful to investigate single ribs behavior and to understand effects linked with camber and toe variations, and sidewalls and inner air implementations, to increase global reliability of the tool.