Quadrature 1D-LiDAR Sensing for Indirect Height Measurement of a Helical Bogie Spring.

Three-dimensional optical ranging has become an effective tool for railway infrastructure monitoring, enabling accurate geometric characterization of tracks and the detection of structural anomalies. Beyond track inspection, this work investigates the potential of a low-cost optical ranging approach for indirect monitoring of railway suspension components. Two low-cost 1D laser ranging sensors arranged in quadrature were used to observe the lateral profile of a helical bogie spring under loading conditions. Owing to the 18° field of view of each sensor, the measured responses exhibited a quasi-sinusoidal dependence on spring height. By applying phase unwrapping to the quadrature signals, the spring height was reconstructed in real time. Two independent vertical displacement tests were performed, achieving mean errors of 0.66 mm and -1.47 mm, with standard deviations of 2.35 mm and 2.16 mm, respectively, demonstrating consistent accuracy and repeatability of the method. The proposed quadrature sensing approach provides a simple, non-contact, and cost-effective solution for indirect estimation of the bogie spring height. It is particularly suitable for installations where direct vertical measurements are impractical and offers a promising method for monitoring spring compression and suspension loading in railway condition monitoring systems.