BIZOMAT MAKEOS · Hydraulics
Accumulator Circuit Sizing (Pump Deficit, Gas Volume, Recharge)
Does this cylinder stroke need an accumulator to reach its speed, how big must it be, and can the pump recharge it before the next stroke?
Sizing of an accumulator to help a pump with a fast cylinder stroke: oil volume and flow for the stroke in the time wanted, what the pump supplies in that time, the deficit the accumulator must deliver, the accumulator gas volume for the precharge, minimum and maximum pressures and the polytropic exponent (as the accumulator size tool), the recharge time at pump flow against the time available, and the installed size against the size needed.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Cylinder bore | mm | Bore of the cylinder (cap-side area is used). |
| Stroke | mm | Stroke length. |
| Cylinders moving together | Number of cylinders that stroke at the same time. | |
| Stroke time wanted | s | Time the stroke must take. |
| Pump flow | L/min | Flow of the pump. |
| Time available to recharge | s | Time between strokes in which the pump refills the accumulator. |
| Precharge pressure | bar | Gas precharge pressure (about 90% of the minimum working pressure for bladder types). |
| Minimum working pressure | bar | Lowest pressure at which the cylinder still does its work. |
| Maximum working pressure | bar | Pressure at which the accumulator is full (relief or unloading setting). |
| Polytropic exponent (1 slow, 1.4 fast) | Exponent of the gas process: 1 for slow (isothermal), 1.4 for fast (adiabatic) discharge. | |
| Accumulator size installed or offered | L | Nominal gas volume of the accumulator considered. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Cylinder bore
- What it is
- The inside diameter of the hydraulic cylinder. The full cap-side area is used to work out the oil volume for the stroke.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stroke volume rises with the square of bore.
- Get it right
- Use the bore, not the rod diameter or outside diameter of the barrel.
What this means: Stroke
- What it is
- The distance the piston travels in the stroke that the accumulator helps to supply.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stroke volume rises in proportion.
What this means: Cylinders moving together
- What it is
- The number of identical cylinders that make this stroke at the same time and draw oil together.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 20. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Stroke time wanted
- What it is
- The time in which the stroke must be completed. The pump and accumulator together must supply the stroke volume in this time.
- Units and format
- Enter a number in s: seconds. The form accepts 0.000001 s to 600 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A shorter stroke time raises the flow needed and the accumulator volume.
- Get it right
- Enter seconds, not minutes.
What this means: Pump flow
- What it is
- The flow the pump actually delivers to the circuit, from the pump data at its running speed and pressure.
- Units and format
- Enter a number in L/min: litres per minute. The form accepts 0.000001 L/min to 10000 L/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 L/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More pump flow reduces what the accumulator must deliver and shortens recharge.
- Get it right
- Use the effective flow at working pressure, not the theoretical displacement.
What this means: Time available to recharge
- What it is
- The time between strokes in which the pump can refill the accumulator.
- Units and format
- Enter a number in s: seconds. The form accepts 0 s to 10000 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter seconds; recharge time is checked against it.
What this means: Precharge pressure
- What it is
- The gas precharge pressure in the accumulator with no oil in it, set with nitrogen. Enter it as a gauge reading; the tool adds atmospheric pressure.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 1000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter gauge pressure; it must be below the minimum working pressure, or the tool stops.
What this means: Minimum working pressure
- What it is
- The lowest system pressure at which the cylinder still does its job. The accumulator delivers oil until it falls to this pressure.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 1000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raising it closer to the maximum pressure reduces the usable oil and needs a larger accumulator.
- Get it right
- Enter gauge pressure; the tool converts to absolute.
What this means: Maximum working pressure
- What it is
- The system pressure when the accumulator is full, set by the relief or unloading valve.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 1000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher maximum pressure increases the usable oil per litre of gas volume.
- Get it right
- Enter gauge pressure; it must not exceed the accumulator’s rating.
What this means: Polytropic exponent (1 slow, 1.4 fast)
- What it is
- The polytropic exponent of the gas process: 1 for slow, isothermal discharge and 1.4 for fast, adiabatic discharge of nitrogen.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 1.67. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Fast strokes are closer to 1.4; using 1 for a fast stroke undersizes the accumulator.
What this means: Accumulator size installed or offered
- What it is
- The nominal gas volume of the accumulator installed or offered, from its catalogue size. It is compared with the gas volume needed.
- Units and format
- Enter a number in L: litres. The form accepts 0.000001 L to 10000 L. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 L as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Stroke volume V = n × π D² ÷ 4 × stroke; flow needed = V ÷ t₁.
- Pump supplies Q_p t₁; deficit ΔV = V − Q_p t₁.
- Gas volume V₀ = ΔV ÷ [(P₀ ÷ P₁)^(1/n) − (P₀ ÷ P₂)^(1/n)] with absolute pressures (as the accumulator size tool).
- Recharge time = ΔV ÷ Q_p, against the time available.
- Example: the stroke needs 45.239 L/min against 30 L/min from the pump; the accumulator supplies 0.50796 L and must be at least 1.4093 L.
Limitations
- Ideal gas; real gas at high pressure needs a correction factor.
- Pressure drop in valves and lines during the fast stroke is not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size an accumulator for a fast clamp or press stroke
- Check whether a smaller pump plus accumulator will do
- Check recharge between cycles
Who it is for
- Hydraulic engineers
- Machine designers
- Maintenance engineers
What you get
- Stroke volume and flow
- Deficit and accumulator size needed
- Recharge time and installed size check
Interpreting the result
- A fast stroke discharges nearly adiabatically: sizing with n = 1 would undersize the accumulator.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 352–368. Topic reference; no source tables or recommended settings are reproduced.
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Open the Accumulator Circuit Sizing (Pump Deficit, Gas Volume, Recharge) calculator