We study rubber friction for tire tread compounds on asphalt road surfaces. The road surface topographies are measured using a stylus instrument and atomic force microscopy, and the surface roughness power spectra are calculated. The rubber viscoelastic modulus mastercurves are obtained from dynamic mechanical analysis measurements and the large-strain effective modulus is obtained from strain sweep data. The rubber friction is measured at different temperatures and sliding velocities, and is compared to the calculated data obtained using the Persson contact mechanics theory. We conclude that in addition to the viscoelastic deformations of the rubber surface by the road asperities, there is an important contribution to the rubber friction from shear processes in the area of contact. The analysis shows that the latter contribution may arise from rubber molecules (or patches of rubber) undergoing bonding-stretching-debonding cycles as discussed in a classic paper by Schallamach.
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In the non-linear response region, if the applied strain oscillates as ϵ(t) = ϵ0cos(ωt), the stress will be a sum involving terms ∼cos(nωt) and ∼sin(nωt), where n is an integer. The DMA instrument we use defines the modulus E(ω) in the non-linear region using only the component f(ϵ0, ω)cos(ωt) + g(ϵ0, ω)sin(ωt) in this sum which oscillates with the same frequency as the applied strain. Thus, ReE(ω) = f(ϵ0, ω)/ϵ0 and ImE(ω) = g(ϵ0, ω)/ϵ0. Note that with this definition the dissipated energy during one period of oscillation (T = 2π/ω) is just as in the linear response region.
The Persson contact mechanics theory is a small-slope theory and it is not clear a priori how accurate the predictions are for the rms slope 1.3. However, a recent study of Scaraggi et al. (unpublished) shows that the small slope approximation is accurate also for surfaces with rms slope of order 1.
See article about rubber friction by K. A. Grosch in Ref. 5.
