Numerical analysis of Hertzian and non-Hertzian wheel-rail contacts

Improved rail car designs which can provide faster, safer and more economical transportation, often require a significant amount of dynamic analysis and simulation. Of the many important processes that simultaneously occur during the rolling of wheels on rails, one of the most important is that of the contact mechanics at the wheel-rail interface. The forces which develop within the contact patch are ultimately responsible for coupling the dynamics of the rail car to the geometry of the rail. This work seeks to understand the mechanics of wheel-rail contacts and to define the governing parameters in a generalized format which can be used for dynamic rail car simulation. Emphasis is given to non-Hertzian contact geometries and the tribological implications of frictional work.;The mechanics of both Hertzian and non-Hertzian contacts were studied with the aid of a variety of computational tools. A detailed parametric analysis was performed for a 136RE X AAR1-B rail-wheel combination. Three different regimes of contact were identified (assuming unworn profiles) between the rail crown and gauge corner. Two were Hertzian and the other was non-Hertzian. Solution to the normal problem for each regime of contact was obtained over a wide range of wheel loads. Using the results of the normal problem, solutions to the tangential problem were obtained for each regime of contact for a wide range of creepages. This was accomplished for the non-Hertzian contact by using both a non-Hertzian algorithm as well as postulating the existence of an ellipticized non-Hertzian contact and treating it with classic Hertzian methods. This latter method showed that the non-Hertzian nature of wheel-rail contacts does not significantly alter the classic creep force - creepage behavior (for non-Hertzian contacts having a geometric distortion of ;Results of the parametric analysis also revealed a set of generalized surface equations capable of approximating both longitudinal and lateral creep force as a function of the creepages and patch aspect ratio. The form of these equations was found to be most accurately represented by the hyperbolic tangent function. Speed and accuracy tests of the approximating functions showed favorable results when compared to other codes that were based on complete creep force - creepage theories.;Generalized approximating equations were also obtained which accurately represented the behavior of global contact patch friction work. The distribution of local patch friction work was also obtained for both Hertzian and non-Hertzian contacts. Due to the asymmetry of traction and slip profiles for the non-Hertzian patch, a unique bi-modal patch friction work profile was obtained.