A Modular Race Tire Model Concerning Thermal and Transient Behavior using a Simple Contact Patch Description
The potential of a race tire strongly depends on its thermal condition, the load distribution in its contact patch, and the variation of wheel load. The approach described in this paper uses a modular structure consisting of elementary blocks for thermodynamics, transient excitation, and load distribution in the contact patch. The model provides conclusive tire characteristics by adopting the fundamental parameters of a simple mathematical force description. This then allows an isolated parameterization and examination of each block in order to subsequently analyze particular influences on the full model. For the characterization of the load distribution in the contact patch depending on inflation pressure, camber, and the present force state, a mathematical description of measured pressure distribution is used. This affects the tire's grip as well as the heat input to its surface and its casing. In order to determine the thermal condition, one-dimensional partial differential equations at discrete rings over the tire width solve the balance of energy. The resulting surface and rubber temperatures are used to determine the friction coefficient and stiffness of the rubber. The tire's transient behavior is modeled by a state selective filtering, which distinguishes between the dynamics of wheel load and slip. Simulation results for the range of occurring states at dry conditions show a sufficient correlation between the tire model's output and measured tire forces while requiring only a simplified and descriptive set of parameters.ABSTRACT
Overview of the different modules of the tire model and their interaction.
Force versus slip. Generic force curve described by the steady state tire force model. Normalized sliding slip
, sliding force
, and cornering stiffness
are marked.
Optimal camber versus side force for different air pressure levels and the loss of tire force potential versus camber error for different wheel load levels. Higher air pressure reduces the optimal camber. Increasing wheel load reduces the effect of camber errors.
Force versus side slip. The additional slip
shifts the complete curve in the x direction. Further the force offset ΔFM shifts the maxima in the y direction.
Change of mechanical properties: Shear modulus G and friction coefficient versus temperature. Shear modulus is monotonically decreasing, the friction coefficient has a maximum over increasing temperature.
Relaxation length and lateral force versus side slip for two different loads (Fz = 1000 N). The relaxation length gets smaller for increasing side slip, while it is getting bigger for increasing wheel load.
Mean tire force potential versus frequency for a sinus shaped wheel load excitation. The loss of tire potential increases with higher oscillation amplitude and higher excitation frequency. The degressive character of the force potential over wheel load leads to a part of the loss that only depends on the oscillation amplitude, but not on the frequency.
Speed and tire surface temperature versus lap completion for the rear left tire over a lap of a Le Mans Prototype on the racetrack Circuit Ricardo Tromo, Valencia. Typical lap times at the racetrack are around 90 seconds.
Side force versus side slip for different wheel speeds and different wheel loads. The time constant changes clearly between the conditions. The graphs show the measured force together with the calculated steady state and transient force.
Speed, calculated tire force, and surface and average core temperature versus lap completion. Measured and calculated surface temperature are close to each other. The measured core temperature is 85 °C. That is slightly lower than the calculated core temperature.
Side force and surface and core temperature versus time taken from simulation and test rig data. The temperature distribution, which is calculated according to the normalized load distribution, correlates with measured temperatures.
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