Mathematical model for two-dimensional dry friction modified by dither.

Abstract

A new dynamic two-dimensional friction model is developed which is based on the bristle theory. Actually it is the Reset Integrator Model converted into a two-dimensional space. Usually two-dimensional friction models are indeed onedimensional models which are rotated into the slip velocity direction. However, this often used approach cannot be applied to the bristle model. That is why an idea of a two-dimensional bristle is presented. Bristle’s deformation is described using polar coordinates. The carried out numerical simulation of a planar oscillator has proved that the new model correctly captures the mechanism of smoothing dry friction by dither applied via perpendicular and co-linear way regarding the body velocity. Furthermore, the introduced mathematical model captures two-dimensional stick-slip behaviour. The Cartesian slip velocity components are the only inputs to the model. In addition, our proposed model allows to describe a friction anisotropy using the bristle parameters. The paper contains results of an experimental verification of the new friction model conducted on the special laboratory rig being used to investigate the two dimensional motion in the presence of dither as well as to validate our numerical results.