Governing equations for the analysis of pressure transient are derived from the principle of conservation of mass and momentum for a pneumatic brake system, which consists of a train pipe connected to a number of linear actuators (brake cylinders with piston displacement). The governing one-dimensional non-linear partial differential equations for the train pipe, non-linear ordinary differential equations for the brake cylinders, and second-order differential equation of motion for piston displacement are solved to determine the pressure transients in the brake system for a step change in pressure at the inlet. The governing equations are nondimensionalized and reduced to a set of ordinary nonlinear differential difference equations and integrated by standard numerical methods. The flow is considered isothermal, and the friction effects for turbulent and laminar flow are evaluated by quasi-steady state approximation. The auxiliary reservoir volume effect is also included. The results are compared with the experimental data obtained on a brake test rig.
Mathematical Model of a Railway Pneumatic Brake System With Varying Cylinder Capacity Effects
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Bharath, S., Nakra, B. C., and Gupta, K. N. (September 1, 1990). "Mathematical Model of a Railway Pneumatic Brake System With Varying Cylinder Capacity Effects." ASME. J. Dyn. Sys., Meas., Control. September 1990; 112(3): 456–462. https://doi.org/10.1115/1.2896164
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