Friction-induced vibration: Should low-order models be believed?

Much of the literature of friction-induced vibration focusses on highly simplified models that may include three or fewer modes to describe the independent subsystems. The degree to which these models approximate the behaviour of fuller models remains largely untested. This paper presents a systematic analysis of an example system to explore its convergence behaviour. First, the sensitivity to variations in contact parameters is considered, shedding light on the variability of experimental results. Second, the number of modes required for a ‘minimal’ model is explored. While three modes can often provide a reasonable local approximation to a more general model, the choice of which three is sometimes counter-intuitive. A method for automatic model reduction is proposed and found to be highly effective. The results challenge the general applicability of the oft-quoted two-degree-of-freedom model of ‘mode-coupling’, and also indicate some reasons for the difficulty encountered in validating models of friction-induced vibration.