Occurrence limit of stick‐slip: dimensionless analysis for fundamental design of robust‐stable systems

In most practical mechanical systems, sliding surfaces are utilised under the assumption that they operate smoothly. Stick‐slip motion can therefore be a serious nuisance that interferes with achieving high performance in mechanical systems. The present paper describes the nature of stick‐slip based on an analysis of a 1‐DOF sliding system. The dimensionless parameters controlling the stick‐slip are clarified by deriving the dimensionless forms of the governing equations. For a friction model that considers the dependence of the kinetic friction coefficient on the relative velocity, we find three types of sliding systems with regard to stick‐slip: the unstable system, the stable system and the robust‐stable system. A criterion is proposed for the fundamental design of robust‐stable systems; if a sliding system is robust stable, no matter how large a disturbance is, the energy of the disturbance is dissipated perfectly, and steady sliding without any vibration is ensured. Copyright © 2009 John Wiley & Sons, Ltd.