Relation between the geometry of rail welds and the dynamic wheel–rail response: numerical simulations for measured welds

The primary mechanisms playing a role in the dynamic wheel–rail response to rail weld irregularities in a ballasted track are pointed out. The concept of P1 and P2 forces for metallurgical rail welds, introduced in a first paper [1] concerning the present research, is further elaborated. The dynamic wheel–rail response is simulated for a number of geometrical rail weld measurements. Results show a good correlation between the gradient of the rail weld geometry and the maximum dynamic wheel–rail contact forces, whereas the correlation with vertical peak deviations is shown to be very poor. Therefore, an assessment method based on the gradient (introducing a speed-dependent quality index [1]) is more consistent than a method based on vertical tolerances. An approximate formula is presented to calculate the maximum dynamic wheel–rail contact force as a function of the train velocity and the maximum gradient of the weld geometry, in analogy to Jenkins’ formulae for calculating P1 and P2 forces at dipped rail joints.