A Numerical Algorithm for Determining the Contact Stress of Circular Crowned Roller Compressed between Two Flat Plates

Abstract

The main purpose of this paper is to explore a numerical algorithm for determining the contact stress when a circular crowned roller is compressed between two plates. To start with, the deformation curve on a plate surface will be derived by using the contact mechanical model. Then, the contact stress distribution along the roller which occurs on the plate surface is divided into three parts: from the center of contact to the edge, the edge and apart from the contact line. The first part is calculated by the elastic contact theorem for the contact subjected to nominal stress between non-crowned parts of roller and plates, the second part is obtained by the classical Hertzian contact solution for the contact between crowned parts of roller and plates, and the third part is simulated as exponential decay. In order to overcome the defect of the half space theorem, in which a plate with infinite thickness is assumed initially, a weighting method is introduced to find the contact stress of the plate with finite thickness. Comparisons with various finite element results indicate that the algorithm for estimating the contact stress of a circular crowned roller compressed between two plates derived in this paper can be a reasonably accurate when a heavy displacement load is applied. This is because the contact area is large under a heavy load, and the effect of stress concentration is smaller in comparison with the case under a light load.