Hertzian Contact Stiffness under Eisenmann Assumptions

In dynamic wheel/rail models, the Hertzian contact stiffness is an important parameter. A track structure and wheel set connected by means of a Hertzian spring is used to describe high frequency vertical vibrations. Unfortunately the Hertzian contact stiffness has been a subject of some dispute by various authors and the suggested values of Hertzian contact stiffness by different authors spread over a wide range between 1,400 and 2,300 kN/mm. In an earlier paper the author used Bousinesque equation for vertical deformation of rail under the center of a circular loaded surface to derive a linearized Hertzian contact stiffness formula. Eisenmann has devised a simplified calculation method for the wheel-rail contact problem with the assumption that all curve radii in the mathematical formulation of the contact problem are infinitely large except the radius of the wheel. Measurements have proven that a simplified two-dimensional calculation under Eisenmann assumptions suffices for wheel diameters between 600 and 1,200 mm. In this paper, a formula for the contact length under Eisenmann assumptions is derived first before deriving a formula for the contact stiffness. The formulation is validated by application on data taking from literature and by comparing Hertzian contact stiffness values with the earlier formula.