Improved indirect measurement of the dynamic stiffness of a rail fastener and its dependence on load and frequency

The dynamic stiffness of rail fasteners has a significant effect on the noise radiated by the rails as well as the vibration transmitted to the underlying structures, such as bridges, tunnels or track at grade. This study investigates the load- and frequency-dependence of a WJ-2A fastener which is commonly used in urban rail transit systems in China. This is a two-stage fastener with a rail pad and a baseplate pad separated by a steel plate. Results are obtained using the indirect measurement method in the frequency range 30 to 1000 Hz. The dynamic stiffness of the individual components is investigated as well as that of the whole fastener system and the combined stiffness of the components is verified by comparison with the whole fastener system. A numerical model of the test rig is used to provide understanding of various artefacts that are observed in the measurements and corrections are proposed to minimise their effects on the measured results. These allow for the differences between the response at the measurement positions and at the ideal positions at the interfaces between the fastener system and the rig. The stiffness magnitude of the rail pad, baseplate pad, and whole fastener system increases strongly with increasing static preload and increases weakly with increasing frequency; it is important to take these effects into account in prediction models for noise and vibration. The damping loss factors are not strongly dependent on preload or frequency. To describe the frequency-dependence, a fractional derivative Kelvin-Voigt (FDKV) model is introduced and is fitted to the dynamic stiffness with the help of a genetic algorithm method. The dynamic stiffness of the whole fastener system is influenced by both the rail pad and the lower baseplate pad. It is important to take account of both of them, as well as the internal resonance of the baseplate assembly which appears at around 1 kHz.