Rubber friction on rough and smooth surfaces

Some rigorous contact mechanics is used in a dynamic stiffness approach to generate a new theory for hysteresis sliding friction on some ideal peak shapes. These were the two- and three-dimensional projections: cylinder, wedge, sphere and cone, configured singly or as a periodic array. The theory is then extended for a ‘single roughness order’ i.e. identical peaks arranged with a randomly distributed envelope. A simple algebraic expression is obtained that is closely linked to the rubber complex modulus, with friction bandwidths extending over several decades. Several other secondary effects are introduced: multiple roughness orders, adhesion, stick-slip behaviour, friction magnification from either moments or atmospheric pressure, as these influence the observed friction bandwidth and amplitude. The sliding friction theory and secondary effects are compared to the measurements of Grosch [K.A. Grosch, The relation between the friction and the visco-elastic properties of rubber, Proc. Roy. Soc. Lond. A 274 (1963) 21–39] and Barquins et al. [M. Barquins, A.D. Roberts, Rubber friction variation with rate and temperature: some new observations, J. Phys. D: Appl. Phys. 19 (1986) 547–563], and are able to account for the friction amplitude and bandwidth for both gum and carbon loaded rubbers.