cyclogramThe force, each way
The air pushes on the piston's whole area to extend, and only on the ring around the rod to retract. Seal friction takes about 12 % of it; the page keeps 0.88.
A_out = π · d² / 4 A_in = π · (d² − d_rod²) / 4 F = p · A · 0.88 p in N/mm²: bar / 10A Ø32 cylinder with its usual 12 mm rod, at 6 bar: 425 N out and 365 N in.
The load ratio
The load ratio is the force the load needs over the force the cylinder makes. Under 0.5 the air sets the speed and the load hardly matters; above it the stroke slows, above 0.8 it crawls and can stall, and at 1 it does not move. The page stretches the time by 1 / (1 − ratio) — an empirical model, indicative above 0.5.
F_load = m·g·sin α + μ·m·g·cos α + F_ext on the extend ratio = F_load / FThe default 20 kg on a level guide with μ 0.1 asks 19.6 N of the cylinder: a load ratio of 0.046. Stood vertical, lifting the same 20 kg, it is 0.462; 30 kg is 0.693 — Close.
The stroke time
A stroke takes the air that fills the barrel — and the tube from the valve — at the supply pressure, counted as free air at atmospheric pressure. The flow the valve and its fittings deliver sets how long that takes; the valve's own delay and the end cushioning add to it.
V_free = (A · s + V_tube) · (p + 1.013) / 1.013 V_tube = π · d_t² / 4 · L t_flow = V_free / (Q · k) t = t_flow / (1 − ratio) + t_valve + t_cushionThe default stroke, 200 mm on Ø32 at 6 bar with 1 m of 4 mm tube, takes 1.20 l of free air; at 100 l/min that is 0.720 s. With the load ratio, the 0.08 s valve delay and 0.05 s of cushioning the extend takes 0.885 s — inside the 1 s this page opens with. The retract, on the smaller rod-side area, takes 0.792 s.
Making it faster
Cut the move time to 0.5 s and the same cylinder is too slow. More air flow is the cure — a bigger valve, a wider or shorter tube, the flow control opened: at 250 l/min the stroke takes 0.432 s. A smaller bore needs less air, if its force still covers the load. A bigger bore helps only when the load ratio is the trouble: lifting 30 kg, Ø40 instead of Ø32 brings the ratio from 0.693 to 0.444 and the stroke from 2.48 s to 2.10 s, though it takes 3.38 l of air per cycle instead of 2.24 l.
The air it costs
Each cycle fills the barrel on both sides of the piston, and the tube each time: 2.24 l of free air for the default. Back to back with its 0.5 s dwell, that is 61.9 l/min — the figure for the compressor, though on a machine the cylinder also waits for the rest of the cycle, which lowers it.
Worked example
| Quantity | By hand | Result |
|---|---|---|
| Area out / in | π · 32² / 4, π · (32² − 12²) / 4 | 804 / 691 mm² |
| Force out / in at 6 bar | 0.6 N/mm² · A · 0.88 | 425 / 365 N |
| Load ratio, extending | 19.62 / 424.6 | 0.046 |
| Free air, extending | (160.8 + 12.6) cm³ · 7.013 / 1.013 | 1.20 l |
| Flow time | 1.20 l / (100 / 60) l/s | 0.720 s |
| Extend | 0.720 / (1 − 0.046) + 0.08 + 0.05 | 0.885 s |
| Retract | the rod side, load ratio 0.054 | 0.792 s |
| Air per cycle | both strokes | 2.24 l |
Questions
Which air flow do I enter?
The flow that actually reaches the cylinder, in litres of free air per minute — the least of what the valve, the fittings and the tube let through. A valve's nominal flow is an upper bound; long thin tubes lower it.
Why is the retract faster?
The rod takes up part of the barrel, so the rod side holds less air to fill. Its force is smaller too, but while the load is light the air, not the force, sets the time.
What is a good load ratio?
Under 0.5 for a quick, steady stroke. Between 0.5 and 0.8 is acceptable for a clamp or a press that only has to arrive; above 0.8 the stroke crawls and can stall. A vertical cylinder lifting a load needs the margin most.
Does the page model the tube?
Its volume, yes: the tube fills with every stroke, which costs air and time. Its flow resistance, no — fold that into the air flow you enter.
How does the cylinder become a bar on a cyclogram?
Step 6 makes the extend the bar's move out, the dwell its stay, and the cylinder's own computed retract its move back.
Sources
- Mechanical and Metal Trades Handbook (Europa-Lehrmittel), pneumatic cylinders — the piston forces at 6 bar. The page's forces meet its table within 1 %.
- ISO 15552 and ISO 6432 — the bore series and the usual rod for each bore.
- The 1 / (1 − ratio) slowdown is an empirical model, indicative above a ratio of 0.5; real stroke times scatter with pressure, temperature and wear.
Related guides
- Axis sizing calculatorThe whole guided flow: motion, mechanism, motor, regeneration, and the move as a bar.
- Move time and motion profilePeak speed, acceleration and jerk from a distance and a move time; trapezoid, triangle and S-curve.
- Belt drive motor sizingPulley and motor speed, reflected inertia, torque, belt force — and the gearbox a belt axis needs.
- Rack and pinion motor sizingPinion and motor speed, the inertia the motor sees, torque, the force at the teeth — and the gearbox.
- Ball screw motor sizingSpeed, reflected inertia, torque per phase, RMS, critical speed and D·N for a ball screw axis.
Every term on this page, defined: the axis and motor sizing glossary.