Calibrating torsional eigenmodes of micro cantilevers for dynamic measurement of frictional forces

TL;DR

This paper presents a method for calibrating torsional eigenmodes of micro cantilevers using thermal noise measurements, enabling accurate frictional force measurements in dynamic experiments.

Contribution

It introduces a universal calibration approach linking torsional and flexural eigenmodes through a constant ratio, validated by theory and simulations.

Findings

The ratio of torsional to flexural mode stiffness is constant for certain cantilevers.

Calibration of torsional modes can be derived from flexural mode calibration.

Results are supported by beam theory and finite element simulations.

Abstract

Non-invasive thermal noise calibration of both torsional and flexural eigenmodes is performed on numerous cantilevers of 10 different types. We show that for all tipless and short-tipped cantilevers, the ratio of torsional to flexural mode stiffness is given by a constant, times the ratio of their resonant frequencies. By determining this constant we enable a calibration of the torsional eigenmode, starting from a calibration of the flexural eigenmode. Our results are well motivated from beam theory and we verify them with finite element simulation.