On the Contact Problem of Cylinders Containing a Shallow Longitudinal Surface Depression

Abstract

Numerical results are presented in this paper for the determination of contact extent and maximum contact pressure for the contact of an elastic cylinder and a rigid cylinder containing a shallow longitudinal surface depression at the center of the contact. The profile of the depression is smoothly connected to the cylindrical surface by means of two arcs of equal radius. Comparison was made between the results of this solution and the well-known Hertzian solution without the depression. An approximate solution is given for the case that the contact under the arcs of small radius is narrow compared with that under the cylindrical surface. As the corner radius approaches zero, the magnitude of the pressure peak occurring at the shoulders of the depression varies inversely with 1/3 power of the corner radius.