Model Reduction of Coulomb Friction Damped Systems Using Singular Perturbation Theory

Abstract

This paper presents an extension of singular perturbation theory for use in the analysis of mechanical systems with dry (Coulombic) friction. Standard singular perturbation techniques cannot be applied due to the discontinuity inherent with dry friction. A methodology is developed to obtain a reduced-order piecewise-smooth model that recovers the slow motion of the system throughout the entire state space. Both a zeroth-order and a first-order approximation are obtained. The method is demonstrated successfully on a numerical example. A proof of the validity of the method is contained in the Appendix.