| In this work, the dynamics of a poppet-type relief valve are studied for the purposes of generating an accurate linear model and stability criterion that may be used in design and simulation of hydraulic systems. This study begins by developing a flow rate model for the fluid flow through the valve. Next, a nonlinear model of the valve system, including the steady and transient flow forces that act on the poppet, is developed. From here, a linearized third order model is produced from which a stability criterion for the system is deduced using the Routh-Hurwitz method. The nonlinear and linearized models are compared using simulation studies. The simulation studies show the accuracy of the linear model. Design sensitivity analysis is performed, and recommendations are made that lead to improved stability characteristics of future valve designs. The linear model is shown to be valid for sufficiently stable systems. The stability criterion is shown to be valid for the system under consideration. |
