The stagnant worn profile in a slipping interface

Addressed is the profile variation of a soft surface (brake pad) when successive wear layers are sliced by means of a hard mating part (brake disc). Before the wear process starts, both the pad original profile and the disc standard profile are assumed given. With a preset normal approach, a single wear operation proceeds via a tangential shear stroke. With a step-wise growing feed, incessant variations in the discrete entries of the probability distribution of the pad profile heights are analyzed. The study puts forth a probabilistic model to simulate each incremental approach by assigning the supplied distribution entries to next taller asperities. The effect of the tangential shear stroke is simulated by a conditional probability expression, which assesses whether or not a pad profile height may be sheared by a likely encountered disc asperity. Each single wear operation results in idling of a specific disc-dependent distribution-entry, being estimated via a recurrence formula. It is found that a wear process should undergo two distinct stages; namely, transient and steady. The short transient stage continues as long as the worn layer thickness is below the profile peak heights. The variable probability distribution then still includes a growing number of idling entries. It is in such an early phase of this stage that significant variations in the height distribution take place, whereas long before its conclusive phase the distribution practically converges to a quasi-stagnant state. At a full-worn-layer and beyond, the distribution is completely replaced by idling entries, reflecting a unique invariable state of the pad profile heights.