Comprehensive model of a rotating flexible wheelset for high-frequency railway dynamics

The development and application of wheelset models that realistically incorporate both flexibility and rotation, constitutes a topic that has recently been active in the literature regarding high -frequency railway dynamics. The main application of these models is the simulation of the rail-way vehicle-track dynamic interaction, which justifies the fact that most of them are formulated using coordinates that do not rotate with the solid (Euler coordinates). Wheelset models based on rotating coordinates are scarce, although they have some practical applications when the vi-bration response at points fixed in the material is required (e.g., to simulate the signal of a transducer that is fixed at a point on the wheelset). The present work provides a global method in the modelling of a flexible and rotating railway wheelset, independent of the coordinates used (fixed or rotating). To achieve this, a compact formulation is developed adopting axisymmetric coordinates through both Lagrangian and Eulerian approaches, which are related by means of a coordinate transformation. The equations of motion that are deduced for both reference frames are linear, which allows the natural frequencies to be obtained as seen from a fixed frame as well as the ones observed for a system that rotates with the wheelset. The relationship between the natural frequencies obtained from both equations of motion is expressed as a closed-form formula that depends on the angular velocity of the wheelset. The model is applied to simulate the response measured by the strain gauges used in load-measuring wheelsets, in which a vertical force is acting in the wheel-rail contact. The results can contribute to establish limits on the use of the instrumented wheelsets based on the angular velocity and the frequency of the force applied in the wheel-rail contact.