A vacuum gripper on a pick-and-place robot. It couldn’t hold a perforated cardboard box. The customer thought the vacuum pump was weak. It was a small venturi ejector. The box leaked. The ejector couldn’t pull enough flow to maintain vacuum against the leak. This is how I size a vacuum system.
The two numbers that matter
A vacuum system needs: enough pressure (depth of vacuum) to hold the part, and enough flow (volumetric flow rate) to compensate for leaks. People size for pressure and forget flow. For a solid, non-porous part (glass, metal), pressure is enough — once the vacuum is pulled, there’s no leak. For a porous part (cardboard, wood, foam), the air leaks through the part. The ejector must continuously pull that leak flow just to maintain vacuum.
The holding force is:
F = ΔP × A × μ
Where ΔP is the pressure difference (atmospheric minus vacuum, in N/mm²), A is the suction cup area (mm²), and μ is the friction coefficient (rubber on cardboard ≈ 0.5). For a single Ø50 mm cup: A = 1,963 mm². At -60 kPa (0.06 N/mm²): F = 0.06 × 1,963 × 0.5 = 59 N. That holds a 6 kg part. For a perforated box, the effective ΔP is lower (the vacuum leaks to -40 kPa). F = 0.04 × 1,963 × 0.5 = 39 N. Holds 4 kg. If the box weighs 5 kg, it drops.
The leak flow
A perforated cardboard box leaks about 5-10 L/min per dm² of contact area. For a 200×200 mm cup (0.04 m²), the leak is about 0.4 L/min. That sounds small, but a small venturi ejector might only pull 5 L/min total. The leak consumes 0.4 L/min, leaving 4.6 L/min to pull vacuum. If the cup has to pull down a volume (the hose, the cavity), the pull-down time is V/Q. For 1 L of internal volume and 5 L/min flow, pull-down time is 12 seconds. That’s too slow. The robot moves before the vacuum is established.
The ejector sizing
| Ejector type | Vacuum flow (L/min) | Use for |
|---|---|---|
| Mini venturi (single stage) | 5-10 | Solid parts, small cups |
| Multi-stage venturi | 20-60 | Porous parts, multiple cups |
| Vacuum pump (electric) | 50-200 | Large systems, continuous |
| Central vacuum system | 500+ | Whole plant, many stations |
For the perforated box, I needed a multi-stage venturi pulling 30 L/min. The leak (0.4 L/min) is negligible. The pull-down time for 1 L volume is 1/30 min = 2 seconds. The robot waits 2 seconds for vacuum, then moves. The box holds. The customer’s mini ejector (5 L/min) was 6x too small.
The safety factor
I size the holding force with a safety factor of 4 for lifting. If the part weighs 5 kg (49 N), the required holding force is 196 N. For rubber on cardboard (μ=0.5), at -60 kPa: F = 0.06 × A × 0.5 = 196. A = 6,533 mm². That’s two Ø65 mm cups (A = 3,318 each, total 6,636). Two cups, not one. The customer had one Ø50 cup. It was half the area needed. Even with perfect vacuum, it could only hold 6 kg — but at 60 kPa on cardboard, it held 3 kg. The box (5 kg) was always going to drop.
The suction cup selection
The cup material matters. For cardboard, a soft nitrile rubber cup (60 Shore A) conforms to the rough surface and creates a better seal. A stiff silicone cup doesn’t conform — it leaves gaps. For oily parts, use polyurethane. For hot parts, use silicone. The cup shape matters too: a bellows cup (with folds) conforms to curved surfaces. A flat cup is for flat, smooth parts. I use flat cups for machined surfaces, bellows for cardboard or curved parts.
The numbers I check: holding force F = ΔP × A × μ with a 4x safety factor, and leak flow vs ejector flow. For porous parts, the ejector needs 5x the leak flow. For pull-down time, internal volume divided by flow should be under 2 seconds. The gripper that dropped the box had one undersized cup on a weak ejector — no amount of pressure adjustment fixes a flow problem.
