On the 1/f noise and non-integer harmonic decay of the interaction of a finger sliding on flat and sinusoidal surfaces

Fluctuations of the frictional force arising from the stroke of a finger against flat and sinusoidal surfaces are studied. A custom-made high-resolution friction force sensor, able to resolve milli-newton forces, was used to record those fluctuations as well as the net, low-frequency components of the interaction force. Measurements show that the fluctuations of the sliding force are highly non-stationary. Despite their randomness, force spectra averages reveal regularities. With a smooth, flat, but not mirror-finish, surface the background noise follows a 1/f trend. Recordings made with pure-tone sinusoidal gratings reveal complexities in the interaction between a finger and a surface. The fundamental frequency is driven by the periodicity of the gratings and harmonics follow a non-integer power-law decay that suggests strong nonlinearities in the fingertip interaction. The results are consistent with the existence of a multiplicity of simultaneous and rapid stick-slip relaxation oscillations. Results have implications for high fidelity haptic rendering and biotribology.