Vibrations Induced by Dry Friction

Abstract

Dry friction between two components in rubbing contact may often be the cause of vibration. This type of behaviour was investigated by means of a model apparatus comprising a disc and a cantilever. A mathematical theory for the oscillation of the system was developed: Lagrange's equations were used and the deflections were expressed in normal co-ordinates. Numerical analysis showed that variation of the coefficient of friction with relative velocity was insufficient to cause the vibration. The instability was due to the manner in which the motions of the components were coupled. The amplitude would grow exponentially until limited by a breakdown of the continuity of contact between the components. A refinement of the theory took account of the flexibility and dissipation of the friction material with which the cantilever was tipped. The experimental work verified the existence of stable and unstable regions as predicted by the theory. The measured amplitudes were so great that continuity of contact could not be maintained, as was to be expected if the suggested mechanism of amplitude limitation was actual. A subsidiary investigation was made of the effect of tightness of the cantilever clamp. The investigation has shown that it should be possible to avoid unwanted vibration in any system merely by careful choice of dimensions in the design.