Numerical analysis of freight wagon rolling dynamics on a classification hump

Shuxrat Djabbarov
Department of Wagons and Wagon Facilities, Tashkent State Transport University, Tashkent 100069, Uzbekistan
Bakhrom Abdullayev
Department of Wagons and Wagon Facilities, Tashkent State Transport University, Tashkent 100069, Uzbekistan
Aziz Gayipov
Department of Wagons and Wagon Facilities, Tashkent State Transport University, Tashkent 100069, Uzbekistan
Abdusaid Yuldashov
Department of Wagons and Wagon Facilities, Tashkent State Transport University, Tashkent 100069, Uzbekistan
Nodir Botir o’g’li Adilov
Department of Wagons and Wagon Facilities, Tashkent State Transport University, Tashkent 100069, Uzbekistan
Irina Soboleva
Department of Wagons and Wagon Facilities, Tashkent State Transport University, Tashkent 100069, Uzbekistan

Article ID: 4108

Keywords: classification hump; freight wagon; longitudinal dynamics; rolling resistance; relative wind; factorial design; uncertainty quantificatio

Abstract

Accurate prediction of freely rolling freight-wagon speed is required to set retarder demand, maintain cut separation, and limit coupling energy in classification yards. This study develops a reproducible one-dimensional model of wagon motion along the first descending section of a classification hump. The governing equation combines the downslope gravitational component, equivalent mechanical resistance, aerodynamic drag based on signed relative air velocity, and rotating-mass inertia expressed through an effective mass. Three modelling levels are compared under identical initial conditions: gravity-only motion, constant mechanical resistance with rotating inertia, and the complete relative-wind formulation. Simulations cover a 60 m section, an initial speed of 0.50 m/s, wagon masses of 68 and 24 t, and track-aligned wind from a 12 m/s headwind to a 12 m/s tailwind. The gravity-only model overpredicts final speed by 7.8–19.7% for the loaded wagon and 3.2–41.3% for the empty wagon. For the loaded wagon, changing from headwind to tailwind raises final speed from 3.869 to 4.295 m/s and reduces travel time from 27.21 to 24.89 s. The time-stepping implementation agrees with the closed-form zero-drag solution to within 0.011%. A complete 2⁴ factorial design identifies wind, gradient, and equivalent resistance as the dominant factors and reveals a substantial wind–mass interaction. A 3,500-run Monte Carlo analysis yields final-speed percentiles of 3.659, 4.074, and 4.403 m/s at P5, P50, and P95, respectively. The model is suitable for preliminary yard assessment and measurement planning; operational use requires yard-specific resistance calibration and independent field validation using separate calibration and validation datasets.

Published

2026-08-18

How to Cite

Djabbarov, S., Abdullayev, B., Gayipov, A., Yuldashov, A., Botir o’g’li Adilov, N., & Soboleva, I. (2026). Numerical analysis of freight wagon rolling dynamics on a classification hump. Sound & Vibration, 60(5). https://doi.org/10.59400/sv4108

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Vol. 60 No. 5 (2026)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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