Vertical dynamic impact forces on railway tracks develop as a result of train speed and vehicle-track interactions. Variations in track profile and track stiffness as well as variations in wheel circularity influence the dynamic impact forces that are mutually transferred between the track and the wheel of a speeding train.
Today, there are various methods for predicting vertical dynamic impact forces. Most of these methods are based on empirical studies, and few others are analytical in nature. These equations can be evaluated under three main categories: equations that concentrate on vehicle properties, equations that concentrate on track properties and equations that consider both the train and the track properties.
This paper presents an analytical equation that is developed based on a new analytical method proposed by Dr. Bezgin from Istanbul University, which explicitly correlates the instantaneous vertical impact forces generated by the wheels of a moving train to train speed, track stiffness and track or wheel irregularities. This paper concentrates on the effects of wheel flats on vertical wheel forces and proposes an equation that estimates the vertical impact forces due to train speed, wheel diameter, track stiffness and the depth and the length of the wheel flat. The proposed equation relies on the principle of conservation of energy, rules of kinematics, geometry, Hertzian contact theory and a new concept of impact reduction factor. The occurrence of the dynamic impact forces at different train speeds and wheel flat dimensions will be investigated based on different wheel diameters and track stiffness values. The results with respect to the effects of wheel flat dimensions on the vertical impact forces will be compared with the limitations for the wheel flats provided in the UIC Code 510.

dynamic impact forces, track irregularities, track stiffness, wheel flats, impact reduction factor