The Cylinder That Couldn’t Push
We specified a Ø32 mm cylinder to push a 5 kg part up a 10° incline. At 6 bar, the cylinder was rated at about 400 N. The required force was maybe 50 N. On the floor, it barely moved. The problem: the actual air pressure at the machine was 4.5 bar, not 6 bar. At 4.5 bar, the cylinder force dropped to 300 N. Still enough for 50 N. But there was friction in the linear guide (dirty, dry) that added 200 N of drag. The total force needed was 250 N, and the cylinder was producing 300 N — barely. It moved slowly and stalled at the end of stroke. We upsized to a Ø40 mm cylinder (producing 500 N at 4.5 bar). It moved fast and had margin. The mistake was calculating the force at 6 bar and ignoring the actual plant pressure and the friction.
Pneumatic cylinder sizing looks trivial: bore from force. But the actual force depends on the real air pressure, the duty cycle, the friction, and whether the cylinder is extending or retracting. This article walks through the numbers I run for every cylinder.
The Force Equation
The cylinder force is the air pressure times the piston area.
F = P × A = P × π × d² / 4
Where P is the air pressure (Pa or N/m²) and d is the bore diameter (m). For retraction, the rod area reduces the effective area: Aᵣₑₜ = π × (d² − dᵣₒ²) / 4.
Step 1: Determine the Required Force
What does the cylinder need to push or pull? Break it down.
- Weight on an incline: F = m × g × sin(θ). For 5 kg on 10°: F = 5 × 9.81 × sin(10°) = 5 × 9.81 × 0.174 = 8.5 N. (This is small.)
- Friction on a linear guide: Fբ = μ × N. For a 5 kg load on a dry guide, μ = 0.1: Fբ = 0.1 × 49 = 4.9 N. (With dirty bearings, μ can be 0.3: 14.7 N.)
- External process force: Pressing, clamping, lifting. If the cylinder presses with 200 N, that’s Fₑₓₜ = 200 N.
For our example: incline (8.5 N) + friction (15 N) + margin = about 50 N required. That’s tiny. But we forgot the process force (the cylinder also has to compress a spring that needs 100 N). Total required force: 120 N.
Step 2: Use the Actual Air Pressure
The catalog says “at 6 bar.” The plant may deliver 5 bar or 4.5 bar. Size for the actual minimum pressure, not the nominal.
Fₐᵥₐᵢₗₐₗₑ = Pₘᵢₙ × π × d² / 4
For Pₘᵢₙ = 4.5 bar (450,000 Pa):
- Ø32 mm: A = π × 0.032² / 4 = 8.04 × 10⁻⁴ m². F = 450,000 × 8.04 × 10⁻⁴ = 362 N.
- Ø40 mm: A = π × 0.04² / 4 = 1.26 × 10⁻³ m². F = 450,000 × 1.26 × 10⁻³ = 565 N.
At 6 bar, the Ø32 would produce 482 N. At 4.5 bar, it drops to 362 N. That’s a 25% reduction. If you sized at 6 bar, you lose 25% of the force when the plant pressure drops.
Step 3: Apply a Safety Factor
Cylinders don’t produce their rated force at speed. At high speeds, the air can’t fill fast enough, and the actual force drops. Also, friction increases as the seals wear. Apply a factor.
- General clamping / low speed: Safety factor 1.5. The available force should be 1.5× the required force.
- Pushing / lifting with load: Safety factor 2.0. More margin for friction and load variation.
- High speed / impact: Safety factor 3.0. The force at speed is lower.
Required force = 120 N. With a 2.0 factor: the cylinder must deliver 240 N. At 4.5 bar, the Ø32 delivers 362 N — that’s enough (362 > 240). But we saw on the floor it stalled. Why? Because the friction was higher than estimated (dirty guide, 30 N not 15 N), and the speed was high (the cylinder moved fast, so the actual force was lower than static). With the real friction and speed, the required force was closer to 300 N. The Ø32 (362 N) had almost no margin. The Ø40 (565 N) had plenty.
| Bore | Force at 4.5 bar (extend) | Force at 6 bar (extend) | Retract (rod 12 mm) |
|---|---|---|---|
| Ø20 mm | 141 N | 188 N | 98 N |
| Ø25 mm | 221 N | 295 N | 162 N |
| Ø32 mm | 362 N | 482 N | 280 N |
| Ø40 mm | 565 N | 754 N | 452 N |
| Ø50 mm | 884 N | 1,178 N | 743 N |
| Ø63 mm | 1,405 N | 1,874 N | 1,227 N |
Step 4: Extend vs. Retract (The Rod Effect)
The retract force is lower because the rod takes up area on the piston. For a double-acting cylinder, the retract force is:
Fᵣₑₜ = P × π × (d² − dᵣₒ²) / 4
For a Ø32 mm cylinder with a 12 mm rod: Aᵣₑₜ = π × (0.032² − 0.012²) / 4 = 6.91 × 10⁻⁴ m². Fᵣₑₜ = 450,000 × 6.91 × 10⁻⁴ = 311 N. That’s 14% less than the extend force (362 N).
If the cylinder pulls a load on retract (e.g., a clamp that opens by retracting), the retract force matters. Don’t size only for extend. A cylinder that extends fine may not retract a heavy load.
Step 5: Air Consumption (Flow Rate)
A bigger cylinder uses more air. The air consumed per stroke is the volume of the cylinder (bore area × stroke) per cycle. At high cycle rates, this adds up.
V = (π × d² / 4) × s
For a Ø32 mm cylinder with 100 mm stroke: V = 8.04 × 10⁻⁴ × 0.1 = 8.04 × 10⁻⁵ m³ = 0.08 L per stroke. At 60 cycles/min, that’s 4.8 L/min. (This is the volume at atmospheric pressure — the actual compressed air use is lower because it’s compressed.)
A Ø50 mm cylinder with 100 mm stroke uses 0.2 L per stroke — 2.5× more air. If the plant compressor is undersized, a big cylinder starves the system. Check the total air consumption when you upsize.
Step 6: Stroke and Buckling
The stroke determines the rod length. A long, thin rod under compression can buckle (bend). The Euler buckling load:
F_buck = π² × E × I / L²
For a steel rod (E = 200 GPa, I = π × r⁴ / 4 for a solid rod). A Ø12 mm rod at 500 mm stroke: I = π × (0.006)⁴ / 4 = 1.02 × 10⁻⁹ m⁴. F_buck = 9.87 × 200 × 10⁹ × 1.02 × 10⁻⁹ / 0.5² = 8,060 N. That’s way above the cylinder force (362 N). No buckling.
But a Ø10 mm rod at 1,000 mm stroke: I = π × 0.005⁴ / 4 = 4.91 × 10⁻¹⁰. F_buck = 9.87 × 200 × 10⁹ × 4.91 × 10⁻¹⁰ / 1.0² = 969 N. Still above 362 N. For strokes over 500 mm, check buckling. If the force is near the buckling load, use a bigger rod or a guided cylinder.
The cylinder sizing workflow: 1) Calculate the required force (weight + friction + process + margin). 2) Use the actual minimum plant pressure (not nominal). 3) Pick a bore where the available force (at Pₘᵢₙ) is 1.5–3× required. 4) Check retract force if the load pulls on retract. 5) Check air consumption. 6) Check rod buckling for long strokes. 7) Add flow controls for speed regulation.
Speed Control: Flow Controls
The cylinder moves too fast (slamming) or too slow. Flow control valves (needle valves) regulate the air flow.
- Meter-out: Control the exhaust air (outflow). This is the standard. The cylinder moves at a controlled speed as the air exhausts through the needle. Use meter-out for most applications.
- Meter-in: Control the supply air. Used for air cylinders that drive a pump or have no load (free flow). For most clamping/pushing, meter-out.
Speed regulation is part of sizing. A cylinder that slams into its end stops wears out. Add flow controls to set the speed.
Mounting and Guidance
A pneumatic cylinder isn’t a guide. The rod extends and retracts, but it doesn’t resist side loads. If the load binds or the cylinder is side-loaded, the rod bushings wear.
- Rodless cylinders: For long strokes where a rod would sag.
- Guided cylinders (twin-piston): Two guide rods resist side loads. Used for pushing/pressing where the load must stay square.
- External guidance: Mount the cylinder on a linear guide. The cylinder provides force; the guide carries the load.
A Cylinder Sizing Checklist
- What is the required force? (Weight + friction + process.)
- What is the actual minimum plant pressure? (Not nominal 6 bar.)
- What safety factor? (1.5 general, 2 lifting, 3 high speed.)
- Pick bore: available force at Pₘᵢₙ > required × factor.
- Check retract force (rod area) if pulling a load.
- Calculate air consumption. (Does the compressor handle it?)
- Check rod buckling for long strokes.
- Is the cylinder guided? (Side loads on the rod?)
- Are flow controls set for speed? (Meter-out.)
- Is the mounting style correct? (Foot, flange, clevis?)
- Does the cylinder need a position switch? (Home/end-of-stroke sensing?)
The Bottom Line
Pneumatic cylinder sizing isn’t picking a bore that “looks” right. Calculate the required force, use the actual minimum plant pressure, apply a safety factor, and pick a bore that delivers. The cylinder that stalled wasn’t undersized at 6 bar — it was undersized at the real 4.5 bar with real friction. Size for the worst case (low pressure, dirty guide, high speed). Add margin. The cylinder that pushes every time isn’t the biggest one — it’s the one sized for the actual pressure and the real friction, not the catalog’s idealized numbers.
