Fundamentals of a reduced elastic friction model

J. Jäger (Jurgen Jaeger)

Lauterbach Verfahrenstechnik, Postfach 711 117, D-76338 Eggenstein, Germany

e-mail: www@JuergenJaeger.de

The fundamentals of a reduced friction principle for general elastic bodies in contact are explained, which simplifies the development of new solutions in contact mechanics. Under consideration of the necessary assumptions by Jдger (2000), the tangential friction problem and the associated mathematical conditions can be reduced to the normal contact problem. The tangential solution results as the difference of the full slip traction for actual contact and a smaller contact area, which represents the stick area (or multiple areas).

The local traction in the slip area opposes the relative motion in the same way as the normal relative approach opposes the contact pressure, as required by Coulomb’s slip inequality. The stick inequality for the traction is identical with the contact condition of positive pressure. This identity is independent of the mathematical form of the contact law. The elastic friction principle can not be regarded as a strict mathematical theorem, because physical applications require the omission of side effects, such as the coupling between the tangential traction components of the classical Cattaneo-Mindlin model. In this article, the force-displacement relation of the elastic friction model is compared with the numerical solution of some examples.