The Screw That Whined at 3000 rpm: Ball Screw Noise, Diagnosed
A rolled ball screw, Ø25 mm, 10 mm lead. At 1000 rpm it was quiet. At 3000 rpm it whined — a high-pitched tone that the operator could hear across the room. The screw wasn’t worn. The preload wasn’t excessive. The speed was above the screw’s critical speed. This is what the whine was, and why the fix wasn’t lubrication.
The critical speed
A ball screw is a long, slender shaft supported at both ends. Like any rotating beam, it has a critical speed — the speed at which it resonates. Below critical speed, it runs smoothly. Above critical speed, it vibrates. The vibration creates noise (the whine) and accelerates wear on the ball nut and bearings.
The critical speed formula for a screw supported at both ends:
N_c = (120·d / L²) · 10⁴ rpm (approximate, for steel)
Where d is the screw diameter (mm), L is the support span (mm). For d = 25 mm, L = 1200 mm: N_c = (120 × 25 / 1200²) × 10⁴ = (3000 / 1,440,000) × 10,000 = 20.8 rpm? That can’t be right. Let me recalculate. The actual formula is:
N_c = (π/2L) · √(E·g·I/ρ·A) × 60 / (2π)
This is getting complicated. The practical rule: a Ø25 screw over 1200 mm span should not exceed about 2000–2500 rpm. We were running 3000 rpm. We were above the critical speed. The whine was the screw resonating.
Why lubrication wasn’t the fix
The customer thought the whine was dry lubrication. We greased the nut. The whine didn’t change. Lubrication affects friction noise (a low rumble, not a high whine). A high-pitched whine at a specific speed is resonance, not lubrication.
If the screw was worn, the noise would be a gritty, rough sound at any speed. If the preload was too high, the screw would run hot (we measured 35°C after an hour, normal). The whine started exactly at 2500 rpm, got louder at 3000, and disappeared when we slowed to 2000. That’s the signature of critical speed.
The fixes
| Fix | Critical speed impact | Cost |
|---|---|---|
| Slow down (max 2000 rpm) | Stays below resonance | Free, but limits speed |
| Larger diameter (Ø32) | Critical speed × (32/25)² ≈ 1.6× | New screw, new nut |
| Center support (3 bearings) | Cuts effective span in half, critical speed ×4 | Mid-bearing housing |
| Ground screw (stiffer) | Slight improvement | Not worth it for resonance |
| Linear motor (no screw) | No resonance at all | High cost |
What we did
We couldn’t slow down — the cycle time required 3000 rpm. We upsized to Ø32 mm. The critical speed of a Ø32 over 1200 mm is about 1.6× the Ø25 — comfortably above 3000 rpm. The whine disappeared. The screw ran quiet at 3000 rpm.
The Ø32 screw was more expensive (about $200 more than the Ø25) and required a new ball nut and new end bearings. But the alternative — a mid-span support — would have complicated the machine design (a support in the middle of the axis limits the travel). The larger diameter was the cleaner fix.
The speed table for ball screws
| Screw diameter | Max speed (1200 mm span) | Max speed (800 mm span) |
|---|---|---|
| Ø16 | ~1500 rpm | ~3000 rpm |
| Ø20 | ~2000 rpm | ~4000 rpm |
| Ø25 | ~2500 rpm | ~5000 rpm |
| Ø32 | ~4000 rpm | ~8000 rpm |
| Ø40 | ~6000 rpm | ~12,000 rpm |
These are approximate. The manufacturer’s catalog has the exact critical speed curve for each screw. The rule: stay below 80% of the catalog’s critical speed at your actual span.
The other noise sources
Not all ball screw noise is critical speed:
- Low rumble: Worn balls or nut. The screw feels rough when turned by hand.
- Grinding sound: Contamination in the nut. Dirt in the ball path.
- Squeal at high speed: Preload too high. The balls are over-loaded in the nut.
- Whine at a specific speed: Critical speed. The screw is resonating.
The speed rule: A high-pitched whine that starts at a specific speed and gets louder isn’t a lubrication problem. It’s critical speed. Check the catalog’s critical speed curve for your diameter and span. If you’re above 80%, upsize the diameter or shorten the span. The screw that whined at 3000 rpm was too thin for the length.
