Deflection Calculation and Dynamic Detection of Non-Uniform Beam via Multi-Point Strain Measurement for Freight Trains

In railway freight transport, the vertical deflection of the load-carrying beam on well-hole car accounts for most clearance intrusions at the bottom when running on curves. This paper proposed a deflection calculation and detection method via in-transit strain measurement at multiple beam locations. First, the theoretical mechanical model between the deflection curve and support strains is built, by defining the variable function of bending moment and second moment of area. Quadratic integration constants are calculated employing the symmetric boundary conditions in angle and deflection. Then, the proposed analytical model is validated by the numerical simulation and on-site experiment. Beam deflections by proposed method deviate from simulation within 4.96%, while that deviation rises to 8.11% in loading experiment due to loading difference. In application, in-transit strain data are collected at the two support bottoms. Dynamic and synthetic deflection of load-carrying beams on different line curves is analyzed by theoretical analysis. The maximum deflection reaches 26.1 mm in dynamic and 65.5 mm in synthetic when the freight train runs on a 405-m radius line curve at the speed of 17.2 km/h. In safety evaluation, maximum rigid transformer displacement is calculated by identified load and measured suspension stiffness coefficient. Considering beam deflection and suspension displacement, the maximum vertical movement of the transformer is 110.4 mm, which does not exceed the allowable distance, 250 mm. Research outcomes demonstrate the effectiveness and reliability of the proposed method, which enables the real-time deflection detection and safety evaluation in freight train transport, as well as estimation of the maximum deflection in forthcoming transport.