There is a type of unloading valve identified as a differential unloading valve. This valve is designed to allow the accumulator to partially discharge before the valve is unvented. Generally, the valve is designed to unvent when the pressure drops 15%. Differential unloading valves are also available that unvent when pressure drops 30%. Unventing means that the piston moves enough to allow the dart to reseat. Once this occurs, the unloading valve functions like a pilot-operated relief valve.
Referencing Fig. 3.17, consider the moment when pressure just reaches 975 psi, and the dart just begins to unseat. Once it cracks open, the pressure in the top chamber cannot increase above 975 psi, so the pressure on one side of the piston (right side in Fig. 3.17) cannot increase above 975 psi. The pressure on the left side can continue to increase up to 1000 psi. This pressure difference causes a force imbalance, so the piston moves to the right, the rod unseats the dart, and the valve is vented.
In a differential unloading valve, the area of the piston is 15% greater than the projected area of the dart. This means that the hydraulic force holding the dart unseated is 15% greater than the hydraulic force that initially unseated the dart. Pressure on the accumulator side must drop 15% below 975 psi before the dart spring can reseat the dart. The force balance is
Pressure on the accumulator side must drop to 848 psi before the valve is unvented.
The symbol used for a differential unloading valve is shown in Fig. 3.19. The vent line connected downstream from the check valve denotes the function of the piston. An accumulator is shown with the symbol in Fig. 3.19 to clarify that the differential unloading valve works with an accumulator.