The Cylinder That Couldn’t Push: Bore Sizing by Force, Not by Guess
A Ø32 mm cylinder pushing a 50 kg slide. It moved the slide slowly, then stalled at mid-stroke. The customer turned up the air pressure from 5 to 7 bar. It moved faster but still stalled. The cylinder was undersized for the load. This is the force calculation that should have been done before ordering.
The force calculation
A cylinder’s push force is:
F = P · A
Where P is the air pressure (N/mm²) and A is the piston area (mm²). For a Ø32 cylinder at 6 bar (0.6 N/mm²): A = π × 16² = 804 mm². F = 0.6 × 804 = 483 N. The slide weighs 50 kg (490 N). The cylinder can’t even hold it, let alone accelerate it. We need a safety factor of at least 2 for pushing a horizontal load (friction + acceleration). Required force: 490 × 2 = 980 N. The Ø32 at 6 bar delivers 483 N. Half what’s needed.
The bore sizing table
| Bore | Area (mm²) | Force at 6 bar (N) | Max horizontal load (N, 2x SF) |
|---|---|---|---|
| Ø20 | 314 | 188 | 94 |
| Ø32 | 804 | 483 | 242 |
| Ø40 | 1257 | 754 | 377 |
| Ø50 | 1963 | 1178 | 589 |
| Ø63 | 3117 | 1870 | 935 |
| Ø80 | 5027 | 3016 | 1508 |
For a 50 kg slide (490 N), we need at least 980 N. That’s a Ø63 cylinder at 6 bar. The customer had a Ø32. It was 4x undersized.
What we did
We replaced the Ø32 cylinder with a Ø63 bore, 100 mm stroke. The push force is 1870 N at 6 bar. The safety factor is 3.8x. The slide moves at full speed, no stalling. The customer didn’t need to turn up the pressure — the cylinder was simply too small.
The pressure doesn’t fix undersizing
Turning up the pressure from 6 to 7 bar gives 17% more force. It doesn’t compensate for a 4x undersized bore. And higher pressure costs more air and wears the seals faster. The correct fix is the right bore size at the rated pressure (6 bar).
The friction coefficient
For a horizontal slide on linear bearings, the friction force is μ × m × g. For μ = 0.005 (profile rail) and m = 50 kg: F_friction = 0.005 × 50 × 9.8 = 2.5 N. That’s negligible. The real force is the acceleration: F = m × a. For a = 0.5 m/s²: F = 50 × 0.5 = 25 N. That’s also small. So why did the Ø32 stall? Because the slide wasn’t on linear bearings — it was on a bushing on a round shaft, which has μ = 0.1. F_friction = 0.1 × 50 × 9.8 = 49 N. Plus acceleration: 25 N. Total: 74 N. The Ø32 delivers 483 N. That should be enough. But the customer’s slide was stuck (not moving freely), so the actual friction was 200 N. Plus the slide was on an incline (a slight slope in the floor). The extra gravity load added 100 N. Total: 300 N. The Ø32 at 6 bar delivers 483 N. It should still work. But at 5 bar (the actual plant pressure), it delivers 402 N. Close to the 300 N needed. The margin was thin. With wear, the friction increased. It stalled.
The bore rule: Size the cylinder for the actual force (friction + acceleration + gravity), not for the weight alone. Add a 2x safety factor. For a 50 kg load on bearings, use Ø50 minimum. Don’t turn up the pressure to compensate for an undersized bore. A cylinder that stalls was the wrong size from the start.
