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This paper investigates the longitudinal dynamics performance of the combined heavy haul trains, especially for the cyclic air braking strategy on the long and steep downhill segments. Firstly, the mathematical models for calculating the longitudinal forces in the longitudinal train dynamics simulations are formulated. The brake delay time between neighbouring cars and the pressure variation of the brake cylinders in the braking and releasing processes are considered in the air braking force model. Besides, the nonlinear hysteresis characteristic of the coupler-draft gear system is taken into account in the coupler force model. The Newmark- β  method is introduced as a numerical solver in this paper. Finally, the simulations based on the real-word infrastructure and vehicle data of the Shuozhou-Huanghua Line are carried out to study the longitudinal dynamics of the combined heavy haul trains with two distributed locomotives.

Study on longitudinal dynamics of heavy haul trains running on long and steep downhills