Contact stresses for closely conforming bodies: application to cylinders and spheres. Final report

Abstract

Since worn wheels and rails contact conformally, the existing contact stress theories for nonconformal contact are not adequate. A general numerical method of solution for three dimensional frictionless, conformal, elastic contact problems is presented. The method is used to analyze the conformal contact of a sphere indenting a spherical seat and a cylinder indenting a cylindrical seat. The results of the sphere-spherical seat problem compared well with experimental data. Results of the cylinder-cylindrical seat problem were in close agreement to a known analytic solution of this problem. For both analyses, results compared favorably with Hertzian theory for problems with small contact regions. A method is given for defining the boundaries of the large contact regions, and for solving the associated governing singular integral equation of the first kind. A general iterative procedure is developed which converges to the true three dimensional contact region. In addition the solution to a non-Hertzian contact problem with a multiply connected contact region is solved; namely, the case of two spheres in contact where one of them has a surface defect or pit.