Study on in-train longitudinal forces of heavy haul trains under emergency braking at gradient change points

Abstract

The braking asynchrony and line complexity pose challenges to safe operation of heavy haul trains. It is of great importance to study the characteristics of longitudinal train dynamics and analyze the distribution of in-train longitudinal forces under the combined effects of various factors and different gradient change profiles. Firstly, mathematical models are established and verified, including an air brake system model with multi-stage nonlinear charging characteristics and a draft gear model with viscous resistance characteristics. These models are used for longitudinal train dynamic computations of a 20,000-ton heavy haul train with the ‘1 + 102+2 + 102 + 1’ marshalling during emergency braking at gradient change points. In addition, the multi-factorial effects of four typical factors with randomness on the longitudinal impulse at gradient change points are analyzed using an orthogonal experiment. The significance of each factor’s effect and the coupling relationship are illustrated. Finally, the longitudinal impulse on four typical gradient change profiles is studied, and the distribution and variation characteristics of in-train longitudinal forces are presented and compared under different braking positions. Computed results show that the effect significance order of each factor on the longitudinal impulse in descending order is response delay time of remote locomotives, braking position, ramp gradient (at the 95% confidence level) and coupling slack (at the 90% confidence level). Moreover, the effects of the factors are independent of one another. The largest longitudinal impulse occurs when the train passes the second gradient change point at 1/2, 1/4, 1/2 and 3/8 of the train length on the ‘U’-shaped, inverted ‘U’-shaped, continuous downhill and continuous uphill profiles respectively. This work develops a valuable method for simulating in-train longitudinal forces and provides theoretical guidance for the safe operation of heavy haul trains in practical engineering.