What is acceptable shaft deflection?

For precision machinery, typical limits are 25–50 μm. For general industrial shafts, up to 0.1 mm may be acceptable. Keep static sag below 10% of bearing radial clearance.

How does shaft deflection affect vibration?

Shaft deflection shifts the center of mass, producing 1× vibration. Excessive deflection can cause rubbing on seals, uneven bearing loading, and instability.

How to reduce shaft deflection?

Increase diameter (deflection ∝ 1/d⁴), reduce bearing span, use stiffer material, add intermediate supports, or use hollow shafts.

Why is moment of inertia important?

The second moment of area I = πd⁴/64 determines bending resistance. A 20% diameter increase reduces deflection by ~52%.

What is the difference between sag and runout?

Sag is gravitational bending at rest. Runout (TIR) includes manufacturing errors and dynamic effects. A perfect shaft still shows runout = 2× sag when rotated slowly.

Free Engineering Tool

Rotor Deflection Calculator

Calculate shaft deflection (sag) on two supports under self-weight and applied loads. Enter shaft dimensions and material for maximum deflection in μm.

Simply Supported Beam Self-Weight + Point Load Steel / Aluminum / Custom

Shaft Length / Bearing Span (mm)

Shaft Diameter (mm)

Material

Additional Center Load — optional (N)

Quick presets

Results

Maximum Total Deflection

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Total Deflection (mm)

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Self-Weight Deflection (δ_max)

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Point Load Deflection (δ_F)

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Shaft Mass

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Moment of Inertia (I)

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Cross-Section Area

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Distributed Load (w)

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Moment of Inertia

Distributed Load

Self-Weight Deflection

Maximum deflection of a simply supported beam under uniform distributed load:

Point Load Deflection

Deflection at center from a concentrated point load:

Total Deflection

Practical Example

Example — Steel Shaft ∅60 × 800 mm

Given: d = 60 mm, L = 800 mm, Steel (E = 210 GPa, ρ = 7850 kg/m³)

I = π × 0.06⁴ / 64 = 6.362 × 10⁻⁷ m⁴

A = π × 0.06² / 4 = 2.827 × 10⁻³ m²

w = 7850 × 2.827×10⁻³ × 9.81 = 217.7 N/m

δ = 5 × 217.7 × 0.8⁴ / (384 × 210×10⁹ × 6.362×10⁻⁷) = 8.66 μm

💡 Tip: Deflection decreases with the fourth power of diameter. Increasing diameter from 50 mm to 60 mm (20%) reduces deflection by ~52%.