Dry Friction Avalanches: Experiment and Robin Hood model

TL;DR

This study combines experiments and theoretical modeling to demonstrate that dry friction stick-slip behavior exhibits self-organized criticality, characterized by power-law distributions and spectra, explained through the Robin Hood model.

Contribution

It provides experimental evidence and a theoretical framework linking dry friction avalanches to self-organized criticality using the Robin Hood model.

Findings

Force jump distributions follow a power law with exponents 2.2 to 5.4.

Power spectrum follows a 1/f^α pattern with α between 1 and 2.6.

Numerical simulations replicate experimental power-law spectra.

Abstract

This paper presents experimental evidence and theoretical models supporting that dry friction stick-slip is described by self-organized criticality. We use the data, obtained with a pin-on-disc tribometer set to measure lateral force to examine the variation of the friction force as a function of time. We study nominally flat surfaces of aluminum and steel. The probability distribution of force jumps follows a power law with exponents $\mu$ in the range 2.2 -- 5.4. The frequency power spectrum follows a $1/{f^\alpha}$ pattern with $\alpha$ in the range 1 -- 2.6. In addition, we present an explanation of these power-laws observed in the dry friction experiments based on the Robin Hood model of self organized criticality. We relate the values of the exponents characterizing these power laws to the critical exponents $D$ an $\nu$ of the Robin Hood model. Furthermore, we numerically solve the equation of motion of a block pulled by a spring and show that at certain spring constant values the motion is characterized by the same power law spectrum as in experiments. We propose a physical picture relating the fluctuations of the force with the microscopic geometry of the surface.