Solution to Hertzian Contact Problem between Wheel and Rail for Small Radius of Curvature

There have been several attempts to solve Hertz equation for curved surface contact problem. One application of Hertzian contact problem is to determine the contact properties between wheel and rail. It is important to understand the contact between wheel and rail so that excessive wear can be avoided and train accidents can be minimized. In this work, an attempt has been made to solve Hertzian contact for small radius of curvature using a simple newly invented formula. A finite element modeling was also performed to observe the variations of maximum contact stress in rail with respect to the change rail radius of curvature. The invented formula was to modify the formula of Fischer et.al especially for the major and minor axis so that a more accurate result was obtained in determining the contact dimensions and maximum contact pressure.