A simple theory of asperity contact in elastohydro-dynamic lubrication

Abstract The Greenwood and Williamson theory of random rough surfaces in contact has been combined with established elastohydrodynamic theory to provide a theoretical approach to highly loaded lubricated contacts in which the load is shared between hydrodynamic pressure and asperity contact. It is shown that, provided a major part of the load is carried by elastohydrodynamic action, the separation between the two rough surfaces is given (to a first approximation) by the film thickness which would exist between two smooth surfaces under the same conditions of load, speed and lubricant. It then follows that the asperity pressure, both real and apparent, is determined primarily by the ratio of theoretical film thickness to the combined roughness of the two surfaces ( h o / σ ). A corollary of this result is that an increase in total load, which has only a small influence on the film thickness, is carried by an increase in fluid pressure and only gives rise to a small increase in asperity contact pressure. By way of example the theory has been applied to two questions. Firstly the time fraction in which there is no asperity contact has been deduced with results which compare favourably with the previous theoretical and experimental work on this problem by Tallian. Secondly, an expression has been found for the number of asperities which become plastic. This is shown to depend upon two parameters: the film thickness to roughness ratio ( h o / σ ) and also upon Greenwood and Williamson's plasticity index.