The mechanism of rolling friction. I. The plastic range

Abstract

This paper describes a study of the friction and surface damage produced when a hard steel sphere rolls between flat parallel surfaces of a softer metal. When rolling first starts, even at small loads there is marked plastic flow of the surfaces and a grooved track is formed. The resistance to rolling is primarily due to the plastic displacement of metal ahead of the ball and may be calculated in terms of the area of the grooved track and the yield pressure of the metal. In the first traversal the ball is supported on the front half of the circle of contact. On rolling back along this track there is no such support for the ball unless it sinks further into the surfaces. This leads to an increase in the width of the groove and further displacement of metal. With successive traversals there is a slow increase in groove width and a gradual decrease in rolling resistance. For metals such as tin which do not work-harden appreciably these changes may be explained quantitatively on the assumption that the area supporting the load remains substantially the same throughout the series of traversals. The rolling resistance throughout this stage is due primarily to plastic displacement and depends little on lubrication. A study of the deformation produced during rolling shows that the centre of the grooved track is very heavily sheared in the direction of rolling, and with repeated traversals this may lead to rapid fatigue of the metal. Here again lubricants have little effect on the rate of fatiguing. As rolling proceeds there is an increase in track width, a slight change in track curvature and, in general, appreciable work-hardening of material within and around the track. As a result of these factors an equilibrium stage is gradually reached (if fatigue failure does not occur first) at which the whole of the load is borne by the ellipse of contact formed by elastic deformation within the width of the existing track. No further appreciable increase in track width occurs, and the rolling friction remains substantially constant for repeated traversals of the track. The rolling friction at this stage is again scarcely affected by lubricants.