Pneumatic Cylinder Force and Air Use

Air cylinder formulas: the extend and retract force from the pressure and the bore, the force with friction losses and the free air used per cycle.

The formulas

D is the bore, d the rod diameter and S the stroke, with p the gauge pressure and pa the atmospheric pressure (1.01325 bar). With the area in mm² and the pressure in bar, the force in newtons is 0.1 × p × A. The retract stroke acts on the annulus area, so its force is lower than the extend force at the same pressure. The efficiency η covers the seal friction and other losses, and it is an example here (0.85), as is every other value. The air volume is that of free air, referred to atmospheric pressure, and it is the figure for the compressor size. The cylinder maker gives the real force and air use, and the end-of-stroke cushions and the lines add to the air use.

Worked example: a 63 mm bore, 20 mm rod, 100 mm stroke at 6 bar

1. A = π × 63² / 4 = 3,117 mm² and Ar = π × (63² − 20²) / 4 = 2,803 mm²
2. Extend force = 0.1 × 6 × 3,117 = 1,870 N, and with η = 0.85 the usable force is 1,870 × 0.85 = 1,590 N
3. Retract force = 0.1 × 6 × 2,803 = 1,682 N

Worked example: free air used by the same cylinder

The pressure ratio is (6 + 1.01325) / 1.01325 = 6.922.

1. Extend: 3,117 mm² × 100 mm × 6.922 = 2.158 L
2. Retract: 2,803 mm² × 100 mm × 6.922 = 1.94 L, so one cycle uses 4.098 L
3. At 10 cycles a minute: 10 × 4.098 = 40.98 L/min of free air

Theoretical force of the 63 mm cylinder by pressure

Frequently asked questions

Why is the retract force lower?

The rod takes up a part of the piston area on the rod side, so the pressure acts on a smaller area.

What is free air?

The air volume at atmospheric pressure. A compressed volume at 7 bar absolute holds about seven times as much free air, which is why the air use is a multiple of the cylinder volume.

Should I use the full theoretical force?

No. Friction and the speed of the stroke use a part of it, and a margin keeps the cylinder from stalling, so the load is chosen well below the theoretical force.

How does this connect to the compressor?

The sum of the air use of all the cylinders, with leakage, is the free air that the compressor must deliver. See the compressor power article for the power.

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