Dependance of the contact area on the velocity of a rolling tire

Tires are made of viscoelastic materials with stiffness quite dependent on the frequency. Generally, two causes of the stiffness increase are distinguished : a frequency dependence complex modulus and a geometrical stiffness. In this paper, an experimental and theoretical study on the relaxation and frequency dependence of complex moduli of the tire constitutive materials are presented and validated. Expressions of the viscoelastic behavior are presented in time and frequency domains. The results show that the real part of the Young's modulus is monotonic according to the frequency. It contributes to an important part of the stiffening. A numerical approach simulating the experimental results of the contact area of Cesbron is also presented. The tire is modeled with a real material distribution in the tire section. The geometrical stiffness also increases with the rotational velocity and it varies with the vibration frequencies. Static and dynamic computations for different rolling velocities are done. The results show that the contact area depends on the velocity of the rolling tire. Comparisons between the measurements and the computations show a good agrement and a decrease of about 20% in the contact areas when the tire rolls compared to a static tire. This difference can be explained by the viscoelastic properties of the materials