On the Use of Geophones in the Low-Frequency Regime to Study Rail Vibrations

Abstract

AimFor a long time, our research team has been successfully using 2Hz geophones to measure vertical velocities and displacements of rails vibrating as a consequence of high-speed train traffic (200 – 300km/h). Our aim is to extend the use of geophones to study vertical vibrations of rails also for lower traffic velocities (as low as possible). The lower the train velocity, the more important the low frequencies to describe the rail vibration. Given that below twice the resonant frequency of the geophone (ωn) the rate |output|/|input| differs significantly from 1, the amplitude of the signal in this frequency interval (0 – 2ωn) must be restored in order to obtain reliable measurements. In this contribution we present a method to correct the amplitude of geophone data in the low-frequency regime, as well as the analysis of “in situ” measurements for testing the goodness of the method. MethodDespite the one-to-one relationship between the spectral amplitude of the input signal and the output of a geophone for frequencies above 2ωn, there are significant phase effects up to 10ωn. This is the reason why phase correction must always be applied. We take advantage of the Discrete Fourier Transform (DFT) to convert the signals from the time domain into the frequency domain. Thus we are able to restore not only the phase but also the amplitude by applying the inverse transfer function of the geophone. The restored data are converted into the time domain by using the inverse DFT. We compare the vertical rail displacements obtained by integrating the amplitude- and phase-corrected velocity measurements with those calculated when only the phase-correction is applied for a rail vibrating when a train travels at 5, 50, 100, 130 and 160km/h. ResultsPreviously to this work, we were able to measure vertical velocities and displacements in rails vibrating as a consequence of high-speed train traffic by using 2Hz geophones. Now, with the new-implemented amplitude correction in the frequency domain, we are also able to obtain these quantities for rails that vibrate when trains with velocity as low as 50km/h travel over them, allowing us to perform studies in underground rapid transit systems.