A hydraulic cylinder converts oil pressure into a straight push equal to pressure times bore area, so at 20 MPa a 50 mm bore gives 39.3 kN, an 80 mm bore 100.5 kN and a 100 mm bore 157.1 kN. Its tube must carry the pressure in its wall: with a wall one quarter of the bore, as the carrier gives for up to 20 MPa, a 50 mm bore at 20 MPa sees 52 MPa in the wall, which is 6.6 to 9.3 times below the tensile strength of plain mild steel.
Part of Hydraulic Systems
A hydraulic cylinder is a tube, a piston and a rod that turn oil pressure into force and oil flow into motion. The same shape appears in pneumatics, with very different behaviour.
Same Shape as an Air Cylinder, Different Behaviour
A hydraulic cylinder and an air cylinder look alike: a piston on a rod in a bore, with ports at each end. They differ in what the fluid does (Hydraulic vs Pneumatic). Oil is incompressible, so a hydraulic cylinder moves exactly as far as the oil put in and stays put when its ports are blocked. Air compresses, so an air cylinder sags under a changing load, and an air cylinder that has been cut off still holds compressed air that can move it. A blocked hydraulic cylinder holds little stored energy in the oil itself, but the load it carries can still fall if a seal or valve leaks.
Size the Bore From the Force and the Pressure
Force = pressure x bore area. To find the bore for a force F at pressure P: bore = √(4 x F / (π x P)).
| Bore | Area | Push at 20 MPa | Tonnes-force |
|---|---|---|---|
| 50 mm | 19.63 cm² | 39.3 kN | 4.0 |
| 80 mm | 50.27 cm² | 100.5 kN | 10.2 |
| 100 mm | 78.54 cm² | 157.1 kN | 16.0 |
Check the 80 mm row: area = π / 4 x 0.08² = 5.027 x 10⁻³ m²; force = 20,000,000 x 5.027 x 10⁻³ = 100,531 N; divided by 9,810 N per tonne-force gives 10.2. The carrier’s 10-tonne example uses 100 kN and gets 80 mm.
Retraction is weaker. The rod takes area from the rod side. An 80 mm bore with a 40 mm rod has a rod-side area of 5.027 - 1.257 = 3.770 x 10⁻³ m², which is 75% of the bore area, so at 20 MPa the pull is 75.4 kN, and for the same flow the rod retracts 1.33 times faster.
The Wall Must Carry the Pressure
Thick-walled tubes follow the Lamé equation (recalled from textbooks): the peak stress is at the bore and equals P x (ro² + ri²) / (ro² - ri²), with ro and ri the outer and inner radii. Worked check of the carrier’s wall rule. For pressures up to 20 MPa the carrier gives a wall of at least 1/4 of the bore, so 12-15 mm for a 50 mm bore:
- ri = 25 mm, wall 12.5 mm, so ro = 37.5 mm
- Peak stress = 20 x (37.5² + 25²) / (37.5² - 25²) = 20 x (1,406 + 625) / (1,406 - 625) = 20 x 2.60 = 52 MPa
- The corpus gives tensile strength for mild steel of 50,000-70,000 psi, 345-483 MPa (Tensile Strength). The ratio is 345 / 52 = 6.6 to 483 / 52 = 9.3
- For cast iron (15,000-30,000 psi, 103-207 MPa) the ratio is only 2.0 to 4.0, and it fails by shattering, so never use it
The corpus’s safety-factor table gives 5-8 for pressure vessels (Safety Factors); 6.6-9.3 on plain mild steel is inside or above that band. The result assumes a known steel with no flaws and no stress concentration at threads, port holes or end-cap grooves, which weaken the tube. Take the tube material from a known source and test the finished cylinder with oil to its working pressure before loading.
Boring the Tube
Use seamless steel tube. The carrier asks for a surface finish better than 0.8 μm Ra and roundness within 0.02 mm. The corpus’s Cylinder Boring article is about steam cylinders and its tolerances are far looser, so use it for the boring-bar method only, not for the roundness figure. The finish matters because the seal rides on the bore; see Seal Systems.
Common Mistakes
- Counting only the tube. The end caps, threads and tie rods carry the full piston force.
- Sizing for push and forgetting pull. The retract force is smaller by the rod area.
- Using a tube of unknown steel. The wall figure depends on knowing the strength.
- Fitting a port in the wall without checking it. A drilled hole is a stress concentration.
Safety
Cylinders hold large forces and fine jets
A cylinder at 20 MPa pushes with tens of kilonewtons, and its end cap carries the same force. A pinhole in the tube, a fitting or a seal throws an invisible jet that injects oil through skin; never search for a leak with a hand, use card or wood, and treat any possible injection as a surgical emergency. A cylinder holding a load can drop it if a seal leaks; block the load mechanically before working near it.
What’s Next
- Learn next: Piston and Rod Design — sizing the rod so it does not buckle
- Combine with: Seal Systems — keeping the oil in