Influences of characteristic size of contact bodies on rolling contact

Abstract

The rolling contact of elastic bodies (upper body and lower body) can be analyzed with the Hertz theory and the Kalker’s model. It is generally believed that the width of the contact area should be much smaller than the characteristic size of each elastic body, to ensure that the half-space assumption is valid. However the definition of “much smaller” is not that clear. In practice the 3x rule is usually employed, which requires the characteristic size of each elastic body must be at least three times larger than the width of the contact area. This empirical rule is examined in this paper, by looking at the results of the Kalker’s model and of a three-dimensional finite element model to study the influences of lower body width on the rolling contact. It is found that the contact behavior predicted by the Kalker’s model are still acceptable even when the characteristic size of contact bodies is close to the width of the contact area. This finding extends the applicability of classical quasi-static methods to a wider scope, and thus may simplify the calculation procedures for rolling contact problems.