Ballscrew Critical Speed Calculator — determine the maximum safe rotational speed for your ballscrew based on root diameter, unsupported length, and end support condition. Also calculates the DN value to check bearing and lubrication limits.
Exceeding ballscrew critical speed causes resonance vibration that can destroy bearings, damage the nut, and ruin surface finish. Even approaching 80% of critical speed introduces measurable whip. This calculator helps you design within safe limits.
Used by CNC machine designers, retrofit builders, and engineers selecting ballscrews for linear motion systems.
Quick Formula
End Support Condition
Ballscrew Dimensions
DN Value Check
Results
How to Calculate Ballscrew Critical Speed
- Identify your end support condition. Fixed-Supported is the most common for CNC (one angular contact bearing block, one simple radial bearing). Fixed-Fixed uses angular contact bearings at both ends and is used for high-speed applications.
- Measure the root diameter of the ballscrew shaft. This is the minor diameter (solid shaft), not the nominal diameter that includes ball grooves. Check the manufacturer datasheet.
- Measure unsupported length — the distance between bearing supports, not the total screw length.
- Apply the formula: Nc = K × droot / L². K depends on the end support: 1.22×10&sup6; (Fixed-Free), 3.04×10&sup6; (Fixed-Supported), 4.88×10&sup6; (Fixed-Fixed).
- Apply safety factor: Multiply Nc by 0.8 (standard) to get the maximum safe operating speed.
- Check DN value: DN = nominal diameter × RPM. Keep below 70,000 for standard ballscrews.
Worked Example
16 mm nominal ballscrew (12.5 mm root), 600 mm unsupported length, Fixed-Supported:
Nc = 3,040,000 × 12.5 / 600² = 3,040,000 × 12.5 / 360,000 = 105.6 RPM
Wait — that seems low. Let us recalculate: 38,000,000 / 360,000 = 105.6. For a 600 mm screw with 12.5 mm root, 105 RPM critical speed is indeed correct. This is why long ballscrews need larger diameters!
Safe RPM = 105.6 × 0.8 = 84 RPM
With 5 mm lead: Max linear speed = 84 × 5 = 422 mm/min — very slow, indicating this screw is too thin for 600 mm span.
Upgrading to 25 mm nominal (21 mm root): Nc = 3,040,000 × 21 / 360,000 = 177 RPM → Safe = 142 RPM → 2,130 mm/min with 15 mm lead
Common Mistakes
- Using nominal diameter instead of root diameter — the root is typically 60-80% of nominal.
- Using total screw length instead of unsupported span between bearings.
- Forgetting that critical speed scales with 1/L² — doubling the length quarters the critical speed.
- Ignoring DN limits — even if critical speed is fine, high DN causes lubrication failure.
Frequently Asked Questions
What happens if I exceed ballscrew critical speed?
The screw enters resonance and begins to whip like a jump rope. This causes violent vibration, destroys bearings, damages the ball nut, and can bend the screw permanently. Even approaching 80% of critical speed introduces noticeable vibration.
What is the difference between fixed-fixed and fixed-supported ballscrew mounting?
Fixed-fixed uses angular contact bearing blocks at both ends, preloaded against each other. This gives 60% higher critical speed and better rigidity, but requires precise alignment and thermal compensation (the screw expands when hot). Fixed-supported uses a simple radial bearing at one end that allows axial float, accommodating thermal growth.
How do I measure ballscrew root diameter?
The root diameter is the minor diameter of the screw shaft — the solid cylinder at the bottom of the ball grooves. Measure with calipers at the groove bottom, or check the manufacturer datasheet. For a 16mm nominal ballscrew, root diameter is typically 12.5-13.5mm depending on ball size.
What is a safe DN value for a ballscrew?
DN = nominal diameter (mm) x RPM. Below 50,000 is safe for any ballscrew with standard grease lubrication. 50,000-70,000 requires oil lubrication or special grease. Above 70,000 requires oil-air or oil-mist lubrication and precision-ground screws.
Can I increase ballscrew critical speed?
Yes: use a larger root diameter, reduce unsupported length (add intermediate supports or shorten travel), or upgrade to fixed-fixed mounting. Increasing screw lead also helps because you need fewer RPM for the same linear speed.
What end support should I use for my CNC?
Fixed-Supported is the best starting point for most CNC builds. It is forgiving of alignment errors and thermal expansion. Use Fixed-Fixed only if you need higher critical speed and can manage thermal compensation (common on production VMCs). Fixed-Free is only suitable for short screws under 300mm.
