Modeling the air brake system equipped with the brake and relay valves

The article presents the mathematical model of the air brake system with two commonly used valves: the dual circuit foot brake valve and the relay valve. The system can be seen as a part of a typical brake system of heavy trucks. The model has been developed based on the previously elaborated and experimentally verified models of the components of the air brake systems. The model can be used at a design stage to predict the behavior of the system during the normal operation and during the sudden braking or malfunction. Differential equations of pressure changes in the chambers and motion equations of the pistons of membrane operated cylinders as well as algebraic equilibrium equations describing the motion of the moving parts of the brake and relay valves are presented. The values of all model parameters, such as, spring stiffnesses and pistons' diameters, etc. have been determined by dismantling the valve or referenced from the literature. The experimental verification of the model is planned in the future.