Mathematical Model of a Railway Pneumatic Brake System With Varying Cylinder Capacity Effects

[+] Author and Article Information
S. Bharath, B. C. Nakra, K. N. Gupta

Mechanical Engineering Department, Indian Institute of Technology, New Delhi-110 016, India

J. Dyn. Sys., Meas., Control 112(3), 456-462 (Sep 01, 1990) (7 pages) doi:10.1115/1.2896164 History: Received April 08, 1988; Revised September 01, 1989; Online March 17, 2008


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.

Copyright © 1990 by The American Society of Mechanical Engineers
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