Dynamical Analysis of a Hydraulic Pressure Relief Valve

A mathematical model is derived that describes the dynamics of a single stage relief valve embedded within a simple hydraulic circuit. The aim is to capture the mechanisms of instability of such valves, taking into account both fluid compressibility and the chattering behaviour that can occur when the valve poppet impacts with its seat. The initial Hopf bifurcation causing oscillation is found to be either superor sub-critical in different parameter regions. For flow speeds beyond the bifurcation, the valve starts to chatter, a motion that survives for a wide range of parameters, and can be either periodic or chaotic. This behaviour is explained using recent theory of nonsmooth dynamical systems, in particular an analysis of the grazing bifurcations that occur at the onset of impacting behaviour.