Nonlinear dynamics and safety aspects of pressure relief valves

Direct spring operated pressure relief valves are regular elements of high-pressure hydraulic systems; however, valve vibrations may still occur endangering the valve and the protected system. The damping of these vibrations is a crucial issue, whereas the external viscous damping at the valve cannot be increased boundlessly based on safety aspects. The vibrations emerge via Hopf bifurcations of either super- or subcritical type, and the nonlinear characteristics have an important role in the valve dynamics. Thorough nonlinear analysis is needed to guarantee safe operation. The linear stability analysis is extended by local and global bifurcation analysis to reveal the stable domains bounded by subcritical Hopf points and the possible bistabilities that exclude the safe operation. Afterwards, the effect of a downstream pipe is analysed, which can also carry safety risks based on the literature; however, the time delay originated in the wave propagation in the pipe may also have stabilising effects. The nonlinear analysis of the presented system compares analytical, semi-analytical and numerical results and assigns the safe parameter domains of the valve with respect to a wide range of relevant parameter variations.