Comprehensive Nonlinear Modeling of a Pilot Operated Relief Valve

Abstract

This paper is directed toward a comprehensive nonlinear modeling and simulation of the performance of a class of a pilot operated relief valves. A mathematical model is deduced to predict the performance of the valve in the steady state and transient modes of operations. The developed model takes into consideration most nonlinearities of the valve and is studied within the MATLAB-SIMULINK environment. The validity of the proposed model is assessed experimentally in the steady state and transient modes of operations. The detailed modeling has resulted in a good agreement between simulation and experimental results. During the simulation studied, it was found that, nonlinearity occurs due to three factors: the pressure changes cause nonlinear velocity changes of the flow rate, the throttling area of the valve restriction usually changes nonlinearly, and the discharge coefficient of the throttling area of the valve restriction does not remain constant. In the transient mode of operation, the simulation studied identified some critical parameters which have a significant effect on the transient response of the valve. Most of the model’s parameters can be evaluated readily by direct measurement of the valve components dimensions thought the Coulomb friction factor and bulk modulus are tuned to match the model to the measurements.