Date of Award


Degree Type



Mechanical Engineering

First Advisor

Richter, Hanz

Subject Headings

Pneumatic control valves, Automobiles -- Pneumatic equipment, Automobiles -- Brakes -- Design and construction, Pneumatic machinery, Mechanical engineering, pneumatic valve pneumatic valve bond graph pressure modulating nonlinear dynamic model simulation


This research develops a mathematical model of the dynamic pressure response to a variable travel input of a pneumatic pressure modulating valve intended for use in a vehicle air brake system. Generically, the valve is a multi-domain system consisting of a mechanical portion and a pneumatic portion. Included in the mechanical portion of the model are compliance of the springs, inertia of the components, and resistance of the sliding components. The pneumatic portion of the model includes capacitance due to the compressibility of the gas, flow resistance through connected plumbing, and flow resistance through the valve control orifices. The development of the mathematical model is accomplished using bond graphs and is complicated by the existence of several sources of non-linearities in the valve being modeled. The non-linearities are the results of mixed modes of operation, fluid dynamics of the gas, use of non-linear springs, and Coulomb friction. First, a bond graph is presented that accurately represents a linear version of the valve. Next the linear state derivative equations are derived. Next, the non-linearities are individually introduced by replacing those linear assumptions with actual, analytically derived non-linear equations and parameters are measured for inclusion in the model. Finally, the model is used to simulate the dynamic response of the valve using a simulation software package.The simulated results are compared to experimental results and found to have good correlation. The model is suitable for use with simulation based design, or as a replacement for an actual valve in a Hardware In the Loop simulator of a vehicle braking system