Determine the short-wavelength roughness cut-off in viscoelastic rubber friction

Determine the physical origin and quantify the precise value of the short-wavelength roughness cut-off λ_min that limits the asperity-scale contributions to viscoelastic energy dissipation in rubber friction for tire tread rubber sliding on road surfaces, specifying how λ_min depends on material properties, surface topography, and operating conditions so it can be used consistently in Persson contact mechanics and related models.

Background

In Persson’s multiscale contact mechanics framework, the viscoelastic contribution to rubber friction on rough surfaces depends on surface roughness over many length scales. For Hurst exponents near 1, each decade of roughness contributes comparably, making the upper wavenumber (short-wavelength) cut-off a critical input.

Experimental analyses suggest that, for tire tread rubber on road surfaces, relevant asperities extend down to micrometer-scale features. However, the physical mechanisms that terminate the cascade of contributing roughness (e.g., contamination layers, run-in induced surface modification, adhesion effects, or material damage) and the precise value of the cut-off remain unclear.

A reliable determination of λ_min is essential for quantitative predictions because all analytical and numerical models require a finite high-wavenumber limit. Establishing its origin and value would remove a key source of uncertainty in theory–experiment comparisons and enable consistent modeling across materials and operating conditions.