A NON-LINEAR FRICTION MODEL FOR SELF-EXCITED VIBRATIONS

The motivation behind this work is to develop a dynamical systems understanding of the phenomenon of squeal. Squeal is a form of self-excited vibration; vibrations are induced in a structure such as a wheel or violin string by the action of a frictional driving force. The nature of this force is rather difficult to define; however, a phenomenological model is proposed which combines the concepts of static and dynamic friction, which seems intuitively reasonable and for which there is documented evidence. In the case presented here, the vibrating structure is simplified to that of a block resting on a moving conveyor belt, restrained by a simple spring and dashpot to a rigid wall. The non-linear system dynamics predicted by using the new friction model are unusual in that the conditions giving rise to squeal include not only the belt speed, but also the initial conditions of the structure. It is thought that this information may be useful in the control of the onset of squeal.