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.
Friction force time series showing irregular fluctuations have been since long considered one of the possible stick-slip regimes in sliding friction. However, it has not been until recently that a 1/f power spectrum in friction force time series derived from sliding friction experiments under wear conditions has been identified. A variety of models, mostly inspired in the field of earthquakes, has been explored, without reaching a fully satisfactory explanation of that behavior. Recently, the present authors have reported results of sliding friction experiments on steel with alumina pins, carried out with and without debris blowing, that proved the role of loose debris in determining the 1/f character of the friction force. A damped-forced harmonic oscillator with two friction terms was proposed to describe the dynamics of friction under wear conditions: one purely random, which accounts for surface roughness, and another inversely proportional to the amount of loose debris that was calculated by means of a modified sand-pile model. This paper presents a full discussion of the experiments that allowed to reach that conclusion and of the model proposed to rationalize the results. In addition, the results of experiments devised to understand the transition from friction with debris to friction without debris (experiment initiated without blowing and after some time switching on blowing) and vice versa are reported. The results of further studies of the wear track are presented, namely, the variation in the track width with sliding distance and results of chemical analyses and surface roughness measurements of the track, for both with or without debris blowing experiments. These additional data give further support to the crucial role of debris in the 1/f character of the friction force.
This article presents experimental results that strongly suggest that the friction force vs time signal in dry friction experiments, carried out under strong wearing effects, shows self-similar fluctuations. Dry friction experiments were carried out in a pin-on-disk machine at loads in the range of 2 to 10 N and linear speeds from 0.05 to 25 cm/s, on SAE 52100 steel and AA5588 aluminum alloy samples. Alumina pins (actually spheres) were used throughout. The power spectra of the friction force vs time signal was obtained by fast Fourier transform (FFT) algorithms, whereas the fractal dimension was calculated by means of a modified box counting method. The results confirm the fractal character (over 3 to 5 decades) and the 1/f b power spectrum of the friction force time series, as well as the well-known relationship D = min [2, (5 -b)/2], valid for self-similar one-dimensional traces. The dependences of the fractal dimension D and the friction coefficient on material and experimental variables (load and speed) are discussed, aiming to identify characteristic trends.
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