Self-Similar Fluctuations and 1/f Noise in Dry Friction Dynamics

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  ^β power spectrum of the friction force time series, as well as the well-known relationship D = min [2, (5 – β)/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.