A rational fraction polynomials model to study vertical dynamic wheel–rail interaction

Abstract

Please cite this paper as: Correa, N., Vadillo, E.G., Santamaria, J., Gomez, J. A rational fraction polynomials model to study vertical dynamic wheel-rail interaction. Journal of Sound and Vibration, Vol. 331, pp. 1844-1858. 2012 Corresponding author. Email: ernesto.garciavadillo@ehu.es Sound and Vibration, Vol. 331, pp. 1844-1858. 2012 NOTICE: This is an electronic version of an article published in Journal of SummaryThis paper presents a model designed to study vertical interactions between wheel and rail when the wheel moves over a rail welding. The model focuses on the spatial domain, and is drawn up in a simple fashion from track receptances. The paper obtains the receptances from a full track model in the frequency domain already developed by the authors, which includes deformation of the rail section and propagation of bending, elongation and torsional waves along an infinite track. Transformation between domains was secured by applying a modified rational fraction polynomials method. This obtains a track model with very few degrees of freedom, and thus with minimum time consumption for integration, with a good match to the original model over a sufficiently broad range of frequencies. Wheel-rail interaction is modelled on a non-linear Hertzian spring, and consideration is given to parametric excitation caused by the wheel moving over a sleeper, since this is a moving wheel model and not a moving irregularity model. The model is used to study the dynamic loads and displacements emerging at the wheel-rail contact passing over a welding defect at different speeds.

On the study of train–track dynamic interactions caused by rail welds on discrete supported rails

“…The model used in the paper has already been validated, and a thorough description may be found in [17]. This model has been adapted to undertake the study presented in this paper.…”

“…The method is based on joint utilisation of the RFP method [19] and optimisation methods using multiobjective genetic algorithms, in order to obtain a system of equations in the spatial domain the behaviour of which is the same as that of a system described by its receptances. The method is comprehensively explained in [17].…”

The time domain moving Green function of a railway track and its application to wheel–rail interactions

“…The second time domain approach is based on the idea of 'mass on time-varying spring' [6][7][8]. Here the time-varying spring represents the track which provides varying dynamic stiffness as a wheel rolls over a sleeper bay.…”

Advanced Techniques for Time-Domain Modelling of High-Frequency Train/Track Interaction

“…Correa et al [138] have applied a modified method of the polynomial rational fraction to transform their track model from the frequency domain to the time domain. The dynamic vertical interaction in the time domain is used to study the dynamic effects arising from the passage of the wheel on rail defective welds.…”