BIZOMAT MAKEOS · Hydraulics
Hydraulic Cylinder Sizing (Bore, Rod Buckling, Flow, Power, Pipes)
What bore and rod does this cylinder need, how much flow and power does it take, and what pipe size suits it?
Sizing a double-acting hydraulic cylinder from the duty: minimum bore for the push force at system pressure, rod diameter for Euler buckling with a mounting factor and safety factor, the largest rod that still gives the pull force, extend and retract flows for the speeds, pump input power and pipe bores for the chosen fluid velocities.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Duty | ||
| Push (extend) force | kN | Force needed when extending. |
| Pull (retract) force | kN | Force needed when retracting. |
| System pressure at the cylinder | bar | Pressure available at the cylinder after losses. |
| Extend speed | mm/s | Extend speed. |
| Retract speed | mm/s | Retract speed. |
| Stroke | mm | Stroke length. |
| Cylinder | ||
| Chosen bore (0 = minimum) | mm | Bore you intend to use (a standard size); 0 shows the minimum. |
| Buckling length (fully extended) | mm | Length used for buckling, usually the fully extended pin-to-pin or mounting length. |
| Effective length factor for the mounting | Effective length factor: about 0.5 fixed–fixed, 0.7 fixed–pinned, 1 pinned–pinned, 2 fixed–free. | |
| Safety factor on buckling | Safety factor applied to the Euler load. | |
| Rod modulus | GPa | Elastic modulus of the rod. |
| Power unit | ||
| Pump overall efficiency | % | Overall efficiency of the pump and motor. |
| Pressure line velocity | m/s | Fluid velocity allowed in pressure lines. |
| Return line velocity | m/s | Fluid velocity allowed in return lines. |
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.
Duty
What this means: Push (extend) force
- What it is
- The force the cylinder must deliver when extending, acting on the full piston area; the rod is also checked for buckling under it.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Minimum bore rises with the square root of the push force.
What this means: Pull (retract) force
- What it is
- The force the cylinder must deliver when retracting, acting on the annulus area around the rod.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0 kN to 100000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger pull force reduces the largest rod that still leaves enough annulus area.
- Get it right
- Enter 0 if there is no pull duty.
What this means: System pressure at the cylinder
- What it is
- The gauge pressure available at the cylinder port after valve and line losses.
- 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 160 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Minimum bore falls with the square root of pressure.
- Get it right
- Use the pressure at the cylinder, not the relief valve setting; 1 bar = 0.1 MPa.
What this means: Extend speed
- What it is
- The piston speed needed while the cylinder extends.
- Units and format
- Enter a number in mm/s: millimetres per second. The form accepts 0.000001 mm/s to 10000 mm/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Extend flow rises in proportion to this speed.
What this means: Retract speed
- What it is
- The piston speed needed while the cylinder retracts.
- Units and format
- Enter a number in mm/s: millimetres per second. The form accepts 0.000001 mm/s to 10000 mm/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 mm/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Retract flow rises in proportion to this speed.
What this means: Stroke
- What it is
- The distance the piston rod travels from fully retracted to fully extended.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Used only for the extend and retract times; the buckling length is entered separately.
Cylinder
What this means: Chosen bore (0 = minimum)
- What it is
- The piston diameter you intend to use, normally a standard size from the cylinder maker.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 2000 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.
- Get it right
- 0 uses the minimum bore for the push force; a value below that minimum is rejected.
What this means: Buckling length (fully extended)
- What it is
- The length used for the rod buckling check, normally the fully extended pin-to-pin or mounting length.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Minimum rod diameter rises with the square root of the buckling length.
What this means: Effective length factor for the mounting
- What it is
- The effective length factor for how the cylinder is mounted and guided, which turns the buckling length into the Euler free length.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 4. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Minimum rod diameter rises with the square root of this factor.
- Get it right
- Take it from the cylinder maker’s mounting chart or an Euler end-condition table.
What this means: Safety factor on buckling
- What it is
- The factor by which the Euler buckling load of the rod must exceed the push force.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Minimum rod diameter rises with the fourth root of this factor.
What this means: Rod modulus
- What it is
- The elastic modulus of the piston rod material, used in the Euler buckling load.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 500 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 206 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A stiffer rod material allows a smaller rod; diameter varies with the inverse fourth root.
- Get it right
- In GPa, not MPa.
Power unit
What this means: Pump overall efficiency
- What it is
- The overall efficiency of the pump and its drive motor, converting the hydraulic power delivered into the input power required.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 10% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 85% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Pump input power is inversely proportional to it.
- Get it right
- Type the percentage itself, not a fraction.
What this means: Pressure line velocity
- What it is
- The fluid velocity you allow in the pressure line, which sets the line bore for the largest flow.
- Units and format
- Enter a number in m/s: metres per second. The form accepts 0.000001 m/s to 15 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher allowed velocity gives a smaller pipe bore.
What this means: Return line velocity
- What it is
- The fluid velocity you allow in the return line, which sets its bore for the largest return flow, including the area-ratio effect.
- Units and format
- Enter a number in m/s: metres per second. The form accepts 0.000001 m/s to 10 m/s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 m/s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher allowed velocity gives a smaller return line bore.
Method and formulas
- Minimum bore = √(4 F_push ÷ π p).
- Rod for buckling: Euler F_cr = π² E I ÷ (K L)² ≥ n F_push, giving d = [64 n F (K L)² ÷ π³ E]^¼.
- Largest rod for the pull force: √[D² − 4 F_pull ÷ π p].
- Flows Q = area × speed; pump power = p Q ÷ η; pipe bore = √(4Q ÷ π v).
- Example: 50 kN at 160 bar needs at least a 63.078 mm bore and a 51.462 mm rod for buckling.
Limitations
- Euler buckling for slender rods; short stiff rods are governed by stress, and cylinder tube support changes the effective length.
- Pressure is at the cylinder; allow for valve and line losses.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Specify a cylinder and power unit for a press or actuator
- Check rod buckling on a long stroke
- Size supply and return lines
Who it is for
- Hydraulic engineers
- Machine designers
- Maintenance engineers
What you get
- Minimum and chosen bore
- Rod diameter limits
- Flows, power and pipe bores
Interpreting the result
- If the buckling rod is larger than the pull force allows, choose the next bore up.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 281–286, 3421–3425. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Rods in machines: cylinders and screws
What it covers: Buckling of hydraulic cylinder rods and screws: the length and mounting that count, why the rod must survive the relief valve's force rather than the duty, and the same check for ball screws.
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Open the Hydraulic Cylinder Sizing (Bore, Rod Buckling, Flow, Power, Pipes) calculator