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Rubber friction on road surfaces: Experiment and theory for low sliding speeds
1.B. N. J. Persson, Sliding Friction: Physical Principles and Applications, 2nd ed. (Springer, Heidelberg, 2000).
5.The Pneumatic Tire, edited by A. N. Gent and J. D. Walter (U.S. Department of Transportation, 2006).
6.H. B. Pacejka, Tyre and Vehicle Dynamics, 2nd ed. (Elsevier, Amsterdam, 2006).
12.S. Westermann, F. Petry, R. Boes, and G. Thielen, Kautsch. Gummi Kunstst. 57, 645 (2004).
36. 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.
41. 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 (unpublished) shows that the small slope approximation is accurate also for surfaces with rms slope of order 1.
45. See article about rubber friction by K. A. Grosch in Ref. 5.
46.B. Lorenz and B. N. J. Persson (unpublished data).
48.It is not clear that the smooth surfaces used by Grosch (and other scientists) are really atomically smooth. Thus, for example, if a glass surface is prepared by cooling a liquid below the glass transition temperature, frozen capillary waves will exist on the surface which may generate a relative large rms slope and which will contribute to the viscoelastic rubber friction. See, e.g., B. N. J. Persson, Surf. Sci. Rep.61, 201 (2006) for a discussion about this point.
49.A. Lang and M. Klüppel, “Temperature and Pressure dependence of the friction properties of tire tread compounds on rough granite,” in KHK 11thFall Rubber Colloquium (2014).
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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
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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