A train air brake force model: Car control unit and numerical results

Abstract

This and a companion paper focus on the integration of a model of a train’s air brake and a non-linear model of a train’s dynamics based on the use of trajectory coordinate formulations. The forces developed by the air brake depend on various system components, including the automatic brake valve, the brake pipe and the car control unit (CCU). The developed braking forces, which depend on the position of handle of the automatic brake valve, are applied to the wheels using the CCU located along the brake pipe and enter into the formulation of the non-linear dynamic equations for the train in addition to other external forces. In order to develop an efficient computational procedure, simplified valve models, with more straightforward operation modes, are considered in order to reduce the computational overhead. The CCU used in this research has a control valve connected to three main pneumatic components: the auxiliary reservoir, the emergency reservoir and the brake cylinder. The reservoirs are the main storage area of the pressurized air, while the brake cylinder transmits the brake force to the wheels using the mechanical components of the CCU, including the brake rigging and the brake shoes. The communications between different parts connected to the control valve are controlled by its slide valve that can be positioned in the brake application, brake release and lap positions. It is also assumed that the CCU modeled in this study has the emergency portion that enables it to apply emergency braking, including the effect of the CCU’s emergency vent valve. In this paper, a mathematical model for the CCU is developed, while the locomotive automatic brake valve and brake pipe models are developed in a companion paper. The relationship between the main components of the air brake system and the train dynamics is discussed, and the final set of differential equations that includes the two models is presented. Furthermore, different computer simulation scenarios are considered in this paper in order to investigate the effect of the air brake forces on the train’s longitudinal dynamics for cases of different braking modes. The numerical results, obtained in this study, are compared with experimental results published in the literature.