Torsional Vibrations of a Cantilever with Lateral Friction in a Resonance Friction Microscope

A model of fundamental torsional vibration of a cantilever with lateral friction is presented by using the harmonic balance method. The model demonstrates that the torsional vibration has close relations with the lateral friction threshold, the lateral contact stiffness and the torsional vibration amplitude of the cantilever. When the threshold is larger than a product of the stiffness and the vibration amplitude, the lateral friction is a linear force with the amplitude. If the lateral friction threshold is less than the product, the motions of the tip on the sample can be stick-slip or slip motions. The results are useful to optimize and to manipulate the fundamental flexural vibration of the piezo-cantilever, and give an insight into the tribological characterization of the interface in a resonance friction microscope.