A significant amount of research has been conducted to select valve timing and area profiles that create efficient and quiet hydraulic pumps and motors. Numerous active valve architectures have been modeled and optimized, but the rationale for the final solution is often unclear. The solution is usually highly dependent on the modeled valve geometry constraints and the duty cycle of the pump or motor for which the valve was optimized. In contrast, this paper proposes a methodology for designing efficient valving that is not constrained to any specific valve geometry, operating point, parameterization, or physical system limitation. An idealized valve area profile is formulated using a piston-cylinder model with variable valve openings. A working fluid that has a pressure dependent bulk modulus is utilized in the model. The valve timing is idealized by constraining it to produce a specified constant pressure drop across the valve. The idealized area profile is synthesized by modeling the piston-cylinder as a pump with passive (check) valves. A representation of the idealized timing is demonstrated for positive pressure differential and positive rotation direction, also known as the first quadrant. The effect of varying pressure on valve timing is shown for the first quadrant, but the trend can be extrapolated for all quadrants of operation. The idealized valve area profile is implemented as fixed valve timing in a pump-motor, meaning the valve area is only a function of the timing angle of the rotating group. Fixed valve timing is preferred to variable valve timing as it can often be implemented mechanically, increasing reliability. The pump-motor is simulated in one rotation direction through a pressure range. Performance is high in pumping operation, but when the pressure differential is reversed, cylinder pressure spikes ensue. Two strategies to modify an idealized valve area profile are presented: timing grooves and a pressure shifted valve timing. Timing grooves reduce pressure spikes and cavitation in the cylinder but generally increase throttling losses. A pressure shifted valve timing has lower throttling energy losses, making it the favored solution.

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