Pressure-flow dynamics with semi-stable limit cycles in hydraulic cylinder circuits

In hydraulic circuits of the standard fluid-power actuators and mechanisms, like the linear-stroke cylinders, some hydrodynamic effects are often neglected. It happens mainly due to their complexity and secondariness in comparison with the principal transient and steady-state behavior of the hydromechanical process variables, such as the differential pressure and relative displacement and its rate, in other words the piston stroke and velocity. However, a constrained motion of the cylinder piston can give rise to the back coupled excitation of the pressure-flow dynamics, especially upon mechanical impact at the cylinder limits. Following to that, semi-stable limit cycles can arise while the hydraulic cylinder remains under pressure without apparent displacement. This paper analyzes such back-coupled pressure-flow dynamics, derived from the partial differential momentum equation with involvement of Darcy-Weisbach hydraulic damping and continuity equation, out from which the closed-form system dynamics is formulated. In both, simulations and laboratory experiments, it is shown that if a constrained motion applies, the solution diverges from steady-state and can develop to the behavior similar to a semi-stable limit cycle.