Accumulator sizing programs are available from many sources on the web and from manufacturers for various accumulator designs. Generally accepted design requirements are that:

  • the gas volume in the bladder should be large enough to prevent the pressure from dropping below a desired minimum level.
  • the accumulator should never run out of oil.

This may seem obvious, yet few accumulators are actually charged such that these two goals are met. Usually, the accumulators have a too low a precharge (not enough gas), much more oil is in the accumulator than is ever used in one operating cycle. This results in the gas volume not being as large as possible. Because the energy storage capacity of the accumulator is proportional to the gas volume, the extra unused oil directly reduces the performance of the accumulator.

Sizing the accumulator accurately is a challenge, even when only one cylinder is involved. To begin, the designer must calculate the flow into and out of the accumulator as a function of time and determine the maximum change in volume from steady state. This requires knowledge of the motion profile of the actuator in order to calculate the amount of oil exiting the accumulator. The power unit pump flow as a function of the pressure should also be taken into account.

Figures 2 and 3 show how the supply pressure and gas volume change as a function of time in a low-duty-cycle example application. In this example, the supply pressure is 1500 psi. The cylinder extend motion occurs between 0 and 1 sec and the retract motion occurs between 2 and 3 sec. During the remaining time the accumulator is recharging to system pressure.

Notice that Figure 3 shows the recharging rate is reduced as the pressure builds back toward the system pressure. This happens when using a power unit with pressure-compensated pump as the pump's displacement control moves back toward its neutral position, and the error reduces between the actual pressure and the compensator pressure setting. These pumps react rather slowly to pressure changes.

An cylinder requiring quick acceleration will demand a high oil flow, making proper accumulator sizing critical. In such a system, the pump may take 100-200 msec to reach full flow — and then only after the pressure has dropped 150 to 200 psi, too late for the acceleration needs of the application. To be conservative in sizing the accumulators, it is best to estimate a generous change in gas volume. Systems using fixed-displacement pumps typically respond faster, so smaller accumulators can be used.

Calculations
Most designers use the ideal gas laws for their accumulator calculations. The ideal gas law,

PV= nRT,
can be stated simply as:
PV = K

Where:

P is pressure of the gas,
V is volume of the gas,
and K is a constant.

However, simple gas laws do not apply when there is little or no heat transferred into or out of the accumulators. Today's hydraulic systems move faster with higher cycle rates. Little time exists for heat to enter or leave the accumulator, so we should assume that the compression and expansion of gas is adiabatic — no heat is transferred into or out of the accumulator. Now the equation becomes more complex.

Where:

P1 is the supply pressure
P2 is the minimum pressure
V1 is the gas volume at steady state,
V2 is the total accumulator gas volume, and
γ is the ratio of specific heat, which is about 1.4 for diatomic gas.

Assume, as in Figure 2, that the system supply pressure is 1500 psi, and we wish to make sure the minimum pressure does not go below 90% (1350 psi). Referring to Figure 3, we see the amount by which the volume changes over time. As a good practice, we add a small safety factor. In the following example calculations — which apply to the similar system graphed in Figures 2 and 3 — one gal of capacity allows for the maximum amount of gas volume change plus the safety factor. This small safety factor ensures the accumulator will not run out of oil.

To calculate the gas volume required for the accumulator, we use the equation

Where
ΔV is the maximum change in gas volume plus a small safety factor. Solving for V1 yields:

This equation can be modified for V1 to obtain:

For this example we assumed the gas or oil volume changed by 1 gal and minimum pressure could not drop below 90% of the supply pressure. Because

13.8 gal is the total accumulator volume required.

In this case, we would use a 15-gal accumulator — the next larger standard size. Notice that the formula only uses the ratio of the pressures, not the absolute values. To limit the system pressure drop to 10%, we need a gas volume approximately 13 times the change in oil or gas volume. Also, note that calculations using the ideal gas law would suggest an accumulator size of 10 gal, which is significantly smaller and could lead to less than optimal motion control results.