Properties of train load frequencies and their applications

A train in motion applies moving steady loads to the railway track as well as dynamic excitation; this causes track deflections, vibration and noise. At low frequency, the spectrum of measured track vibration has been found to have a distinct pattern; with spectral peaks occurring at multiples of the vehicle passing frequency. This pattern can be analysed to quantify aspects of train and track performance as well as to design sensors and systems for trackside condition monitoring. To this end, analytical methods are developed to determine frequency spectra based on known vehicle geometry and track properties. It is shown that the quasi-static wheel loads from a moving train, which are the most significant cause of the track deflections at low frequency, can be understood by considering a loading function representing the train geometry in combination with the response of the track to a single unit load. The Fourier transform of the loading function describes how the passage of repeating vehicles within a train leads to spectral peaks at various multiples of the vehicle passing frequency. When a train consists of a single type of repeating vehicle, these peaks depend on the geometry of that vehicle type as the separation of axles on a bogie and spacing of those bogies on a vehicle cause certain frequencies to be suppressed. Introduction of different vehicle types within a train or coupling of trainsets with a different inter-car length changes the spectrum, although local peaks still occur at multiples of the passing frequency of the primary vehicle. Using data from track-mounted geophones, it is shown that the properties of the train load spectrum, together with a model for track behaviour, allows calculation of the track system support modulus without knowledge of the axle loads, and enables rapid determination of the train speed. For continuous remote condition monitoring, track-mounted transducers are ideally powered using energy harvesting devices. These need to be tuned to optimise energy abstraction; the appropriate energy harvesting frequencies for given vehicle types and line speeds can also be predicted using the models developed. & 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).