Hydraulic actuator sizing engine for machine designers and maintenance engineers: required bore from force and pressure with mechanical efficiency, ISO 3320 standard bore selection, push/pull force at working and relief pressure, flow demand from speed, and Euler rod-buckling verification with mounting-condition factors — every input with selectable universal units and reference-standard values, every report with the full audit trail.
SectorCalc SC-040 sizes a hydraulic cylinder from the load side: required piston area from force, pressure and mechanical efficiency, rounded up to the next ISO 3320 standard bore, with push and pull force at working and relief pressure, pump flow demand for a target speed, and a full Euler buckling check on the piston rod using mounting-condition effective-length factors. The engine sizes on the weaker direction you select (push or pull) so the cylinder meets the load case that actually matters. Results are reference-grade sizing estimates — final selection must be confirmed against the manufacturer's catalog ratings, cushioning requirements and stop-tube guidance for long strokes.
Pressure in MPa equals N/mm², so force in newtons is simply pressure × area — scaled by mechanical efficiency η (0.85–0.95) that covers seal and guide friction. Undersizing pressure margin is the most common cylinder error: a cylinder working continuously at its relief setting overheats the oil, wears the pump, and leaves no reserve for load peaks.
The required diameter is rounded UP to the next ISO 3320 standard bore: 25, 32, 40, 50, 63, 80, 100, 125, 160, 200, 250, 320 mm. Standard bores keep seals, tubes and pistons off-the-shelf — a "62 mm" calculated bore becomes a 63 mm catalog cylinder at no penalty, while a custom 70 mm bore costs weeks and premium pricing.
The retract side always delivers less force because the rod occupies area. With a typical rod ratio dr/D ≈ 0.6, pull force is about 64% of push force at the same pressure. If the working load acts in retract (press return, lift-lowering with resistance), sizing must be done on the annulus — SC-040's direction selector handles exactly that, and flags rods that are disproportionately large for the bore.
Retract is faster than extend at the same pump flow (smaller area). Above roughly 500 mm/s, seal wear, heat and end-stroke impact rise sharply — large bores at high speed need cushioning and often regenerative circuits. SC-040 reports both flows and warns beyond the seal guideline.
In push duty the extended piston rod is a column. At the relief-valve pressure the cylinder can apply its maximum force exactly when the rod is most extended — the worst buckling case:
| Mounting condition | K | Effective length |
|---|---|---|
| Both ends pivoted (clevis–clevis) | 1.0 | 1.0 × stroke |
| One end fixed, one pivoted | 0.7 | 0.7 × stroke |
| Both ends fixed / rigid guided load | 0.5 | 0.5 × stroke |
| One end fixed, load end free | 2.0 | 2.0 × stroke |
Euler assumes the rod carries the load axially through its centerline. Side load, misalignment or a guided load that shares the thrust invalidate the simple check — long-stroke cylinders typically need a stop tube, and heavily misaligned installations need the manufacturer's buckling curves, which include the cylinder body's own stiffness.
Standard industrial cylinders are rated 160, 210 or 250 bar continuous; mobile equipment runs 250–350+ bar. The relief valve must be set above working pressure (typically +10–25%) but within the cylinder's rated pressure — and it is the relief setting, not the working pressure, that defines the buckling and structural worst case. SC-040 validates pmax ≥ p and warns above 210 bar so tube, seals and port ratings are confirmed.
| Bore D | Push area | Typical rod | Push force @ 160 bar, η=0.9 |
|---|---|---|---|
| 25 mm | 491 mm² | 12–18 mm | 7.1 kN |
| 40 mm | 1,257 mm² | 18–28 mm | 18.1 kN |
| 63 mm | 3,117 mm² | 28–45 mm | 44.9 kN |
| 80 mm | 5,027 mm² | 36–56 mm | 72.4 kN |
| 100 mm | 7,854 mm² | 45–70 mm | 113 kN |
| 125 mm | 12,272 mm² | 56–90 mm | 177 kN |
| 160 mm | 20,106 mm² | 70–110 mm | 290 kN |
| 200 mm | 31,416 mm² | 90–140 mm | 452 kN |
On the retract stroke oil acts on the annulus — piston area minus rod area. With a typical rod at 0.6× bore diameter, annulus area is about 64% of full bore area, so pull force is about 64% of push force at the same pressure. If the working load acts in retract, the cylinder must be sized on the annulus or it will stall on return.
When the slenderness is high: long stroke, small rod, push duty, and high relief pressure together. As a screen, when K·S/dr exceeds about 50, check buckling before anything else. Mounting matters enormously — a free load end (K = 2.0) quadruples effective length and cuts buckling capacity to a quarter versus pinned-pinned at the same stroke.
Because the relief valve defines the maximum force the cylinder can ever apply. A stalled or overloaded actuator drives system pressure to the relief setting with the rod fully extended — the exact worst buckling case. Designing to working pressure alone leaves no protection against a blocked load bending the rod.
Seal, guide and bearing friction inside the cylinder — typically 5–15% of theoretical force. It does not cover hose and valve pressure drops (reduce available pressure at the port), volumetric losses (affect speed, not force), or side-load friction from misalignment, which can exceed seal friction many times over. Use 0.85 for aged or side-loaded installations.
A stop tube is a spacer on the piston that increases the distance between piston and rod guide at full extension, reducing guide bearing loads and improving buckling behavior on long strokes. Rule of thumb: consider it beyond about 1 m of stroke in pivoted mounting, or whenever the manufacturer's buckling curves show marginal safety. It shortens usable stroke by its own length — account for it in the layout.
