Continuous assessment of longitudinal temperature force on ballasted track using rail vibration frequency

In this study, the possibility of using the rail vibration frequency to assess the longitudinal temperature force on the rail of ballasted track was investigated experimentally. An empirical formula was subsequently derived to link the frequency index to multiple factors, including the longitudinal temperature force, under-rail stiffness, and fastener spacing. Further tests were conducted to analyse the applicability and accuracy of the frequency index in continuous longitudinal force measurements under different line conditions (i.e. in the non-expansion zone and expansion zone). A technique for using the frequency index to assess the longitudinal temperature force was finally developed. The main results are as follows. (1) The first-order pinned–pinned modal frequency and peak frequency of the mid-span response are very close, and they both change linearly with the longitudinal temperature force on the rail. The rate of change in the vertical direction is larger than that in the horizontal direction. (2) Even if influenced by multiple factors, the peak frequency of the rail mid-span response is suitable for continuous longitudinal temperature force assessment under appropriate measures, and longitudinal temperature force detection could be realized with proper preparation. (3) Using the mid-span response frequency to detect the temperature force of rail located in the expansion zone causes deviation of the results, and under-rail materials whose stiffnesses are insensitive to temperature help reduce this deviation.