Mathematical Modeling of Coupled Wagon Movement on a Railway Hump

Abstract

The efficiency of classification yards is largely determined by the process of controlled humping of railwagons. This paper proposes a mathematical model for calculating the group speed of several coupled wagons (cuts) as they move over a hump. The proposed model is formulated as a Cauchy problem for the Cauchy problem for a Riccati-type nonlinear differential equation, taking into account the basic and additional specific rolling resistance of the wagons, which depend on their mass, type, and operating conditions. Both the forward problem (determining the speed at the end of the hump for a given initial speed) and the inverse problem (determining the required initial speed to achieve a specified speed at the end of the hump) are considered. The proposed approach enables numerical experiments using Euler and Runge–Kutta methods. The results can be applied in the design and operation of modern automatic control systems at classification yards, contributing to increased productivity, energy efficiency, and operational safety.