Tire tread block dynamics

Abstract

Temperature has a crucial influence on rubber friction and tire dynamics. The temperature field in a rubber tread block is the sum of the background temperature $T_0({\bf x},t)$, which varies slowly in time and space, and the flash temperature $ΔT({\bf x},t)$, which in nonzero only close to the macroasperity contact regions, and which varies rapidly in time often on the millisecond time scale. Here we study the motion of a single tire tread block and how it is influenced by the flash temperature. We also present a theory and experimental results for the size of the macroasperity contact regions. In particular, we show that for a large enough nominal contact area, in most cases the diameter $D$ of the macroasperity contact regions are nearly independent of the elastic modulus and the nominal contact pressure.

Figures (15)

• Figure 1: If the nominal contact pressure is small enough the contact between a rubber block and a road surface consist of well-separated macroasprity contact regions. Each macroasperity contact region consist of closely spaced microasperity regions. When calculating the flash temperature the frictional energy produced in a macroasperity contact region is smeared out within the macroasperity contact area to form a laterally uniform heat source. This is a good approximation unless the sliding speed is very high where the heat diffusion is to slow too smear out the temperature profile laterally.
• Figure 2: (a) The real and imaginary part of the viscoelastic modulus $E(\omega)$ as a function of frequency (log-log scale) and (b) the ratio ${\rm Im}E/{\rm Re}E$ as a function of the logarithm of the frequency. For a racing tire tread compound with the glass transition temperature $T_{\rm g} = - 15^\circ {\rm C}$.
• Figure 3: The calculated viscoelastic contribution to the friction coefficient as a function of the logarithm of the sliding speed for the temperature $T=60^\circ{\rm C}$. For the racing compound sliding on a concrete surface. The upper curve denoted $\mu_{\rm cold}$ is without the flash temperature and the lower curve denoted $\mu_{\rm hot}$ is with the flash temperature.
• Figure 4: Calculated results for a rubber tread block sliding on a concrete surface. The upper surface of the rubber block is glued to a rigid surface which moves with the speed $v_{\rm t}=0.1 \ {\rm m/s}$ for the time period $0 < t < 5 \ {\rm ms}$ and with $v_{\rm t}=2 \ {\rm m/s}$ for the time period $5 < t < 10 \ {\rm ms}$. (a) shows the time dependency of the top surface velocity $v_{\rm t}$ (dashed line) and the velocity $v_{\rm b}$ of the bottom surface, which is in contact with the concrete surface. (b) shows the stain and (c) the shear stress in the rubber block as a function of time.
• Figure 5: The dependency of the effective friction coefficient on the velocity $v_{\rm b}$ of the bottom surface of the rubber block. The green lines shows the steady-state friction coefficients without (upper curve) and with (lower curve) the flash temperature. The blue curve is the friction coefficient experienced by the rubber block for the sliding case in Fig. \ref{['one.pdf']}, and the red curve for a similar case but where the sliding speed increases from $0.1$ to $10 \ {\rm m/s}$ at $t=5 \ {\rm ms}$ instead of $2 \ {\rm m/s}$ as in Fig. \ref{['one.pdf']}. The dynamic friction coefficient first follows the cold-branch $\mu_{\rm cold}$ but after sliding a distance of order the size of the macroasperity contact, which is needed to fully develop the flash temperature, it transition to the hot branch $\mu_{\rm hot}$.