Quantification of dynamic wheel–rail contact forces at short rail irregularities and application to measured rail welds

An analytical model for dynamic wheel–rail interaction at rail surface irregularities of arbitrary shape is presented. The model is formulated in the frequency domain and leads to relatively simple closed-form solutions for the variables which describe the dynamic interaction. With the help of the model, basic features of the dynamic wheel–rail interaction at short rail irregularities are identified. The focus is placed on short irregularities with a broad-band spectrum. The model is applied to calculate dynamic wheel–rail contact forces for a sample population of measured rail welds. General quantitative relationships between the rail geometry, the train speed and the level of the dynamic contact force are derived. Statistical distributions of geometrical properties of rail welds and the corresponding contact forces are derived. This allows for an easy estimation of the level of dynamic forces occurring over a railway network, given the availability of geometrical measurements.