Next, the precharge pressure must be calculated. The more difficult part is compensating for the change in temperature between the time the accumulator is charged and when the accumulator is operational. We assume this process will take time, so plenty of opportunity will exist for heat transfer between the oil and the gas. The equation we will use is the ideal gas law.

P V = n R T

The value of n is a constant, and T is temperature. However, this temperature is in degrees Rankin or, which is referenced to absolute zero, so roughly 460° must be added to °F.

The equation we will use is:

The 0 subscript indicates the precharge state, and the subscript 1 indicates the operational, steady state.

Assume the supply pressure is 1500 psi, the operating temperature, T1, is 120° F and the precharge temperature, T0, is 70° F. Now we can calculate the precharge pressure by solving the above equation for P0:

Replacing V1 with V0 - ΔV, and plugging in the numbers from above yields a pre charge pressure of:

P0 = 1279 psig.

Placing accumulators
Accumulators should be mounted as close as possible to where the energy is being used, not where it is being generated. This placement will reduce the pressure losses between the accumulator and the valve. Another consideration is that the flow between the pump and the accumulator is averaged out somewhat over a period of time. The peak flows will occur between the accumulator and the valve, so it is best to keep this distance short.

Even the most capable motion controller may not be able to compensate for a poorly designed hydraulic circuit, and the selection and location of accumulators is key to helping the motion controller do its work precisely.

Conclusions
Among the least understood system elements, accumulators have many purposes in hydraulic motion control applications. Three of the most important roles are storing energy, keeping the supply pressure constant and reducing shock. Storing energy allows for time averaging of the power demands resulting in reduced costs by using fewer and smaller pumps and motors. Keeping the supply pressure constant keeps the gain of the hydraulic system constant which makes the actuators easier to control. Finally, the ability to very effectively absorb shock protects both the hydraulics and the associated mechanical parts leading to longer machine life.