It has been shown that the friction force time series in sliding friction under wear conditions is self-similar and has a $1/f$ power spectrum. Albeit a variety of models, mostly inspired in the field of earthquakes, has been explored, an important factor was overlooked: the role of debris. This Letter describes sliding friction experiments on steel with alumina pins, carried out with and without debris blowing, that prove the role of loose debris in determining the $1/f$ character of the friction force. A damped-forced harmonic oscillator with two friction terms, one purely random and another inversely proportional to the amount of loose debris, calculated by means of a modified sandpile model, is proposed to describe the dynamics of friction under wear conditions.

• Received 13 September 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.045501