Friction dynamics: displacement fluctuations during sliding friction

We have investigated the fluctuations (noise) in the positions of rectangular blocks, made from rubber or polymethyl methacrylate (PMMA), sliding on various substrates under constant driving forces. For all systems the power spectra of the noise exhibit large low-frequency regions with power laws, <i>ω</i>^-<i>γ</i>, with the exponents <i>γ</i> between 4 and 5. The experimental results are compared to simulations and analytical predictions using three models of interfacial interaction: a spring-block model, an asperity-force model, and a wear-particle model. In the spring-block model, small sub-blocks (representing asperity contact regions) are connected to a larger block <i>via</i> viscoelastic springs and interact with the substrate through forces that fluctuate randomly in both time and magnitude. This model gives a power law with <i>γ</i> = 4, as also observed in experiments when no wear particles can be observed. The asperity-force model assumes a smooth block sliding over a randomly rough substrate, where the force acting on the block fluctuates in time because of fluctuations in the number and size of contact regions. This model predicts a power law with the exponent <i>γ</i> = 6, which disagrees with the experiments. We attribute this discrepancy to the neglect of load redistribution among asperity contacts as they form or disappear. The wear-particle model considers the irregular dynamics of wear particles of varying sizes moving at the interface. This model also predicts power-law power spectra but the exponent depends on two trapping-release probability distributions. If chosen suitably it can reproduce the exponent <i>γ</i> = 5 (which corresponds to 1/<i>f</i> noise in the friction force) observed in some cases.