•M. Müller¹, Th. Schimmel¹, H. Fettig², P. Häussler², O. Müller² und A. Albers^2
1Institut für Angewandte Physik, Universität Karlsruhe, D-76128 Karlsruhe, Germany
²Institut für Maschinenkonstruktionslehre und Kraftfahrzeugbau, Universität Karlsruhe, D-76128 Karlsruhe, Germany

To examine tribological properties of surfaces such as friction and wear using atomic force microscopy (AFM), it is necessary to quantify the mechanical deformations of the cantilever during the scanning process and particularly the force constants for tip displacements in the three spatial directions. Since thickness and therefore stiffness varies significantly from cantilever to cantilever due to imperfections within the production process, they are not known and furthermore not easily to obtain by experiment.

In this presentation, a fully parameterized finite element model for V-shaped cantilevers is shown. Individual geometric dimensions of the cantilever can be considered. Using this model it is possible to calculate the force constants and detection sensitivities for both, bending motion normal and parallel to the cantilever, and the torsional motion.

Taking into account that cantilevers in most atomic force microscopes are not mounted parallel to the surface of the sample, also the effective force constants which act parallel and normal to the sample surface can be calculated as a linear combination of the two fundamental bending force constants of the cantilever. Finally the significance of cross talk between bending and torsion is investigated.