What is critical speed?

Critical speed is the rotational speed at which a shaft's rotational frequency equals one of its natural bending frequencies, causing resonance. At critical speed, even small unbalance produces large vibrations that can damage bearings, seals, and the shaft itself.

Why avoid operating near critical speed?

Operating near critical speed amplifies vibrations exponentially due to resonance. The standard practice is to operate at least 20–30% below or above the critical speed. The region within ±20% of critical speed is called the critical speed band and should be avoided.

How to raise critical speed?

Critical speed can be raised by increasing shaft diameter (raises stiffness by d⁴), using a stiffer material (higher E modulus), reducing shaft length, reducing rotor mass, or changing support conditions from simply supported to fixed-fixed.

What is the difference between rigid and flexible rotor?

A rigid rotor operates well below its first critical speed (typically below 70% of Ncr). A flexible rotor operates above its first critical speed and must pass through resonance during run-up and coast-down. Flexible rotors require more careful balancing.

What safety margin is recommended?

API 610 and API 617 recommend that the first critical speed be at least 20% above the maximum continuous operating speed (for rigid rotors) or that operating speed be at least 15–20% above the critical speed (for flexible rotors passing through resonance).

Free Engineering Tool — #009

Rotor Critical Speed Calculator

Calculate the first critical speed (natural frequency) of a shaft with central mass or distributed mass using the Rayleigh method. Compare with operating RPM for safety margin.

Central Mass Rayleigh Method 3 Support Types

Shaft Length L (mm)

Shaft Diameter d (mm)

Rotor Mass m (kg)

Material (E Modulus)

Support Type

Operating Speed (RPM, optional)

Quick presets

Results

Critical Speed (Central Mass)

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Natural Frequency

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Angular Frequency ω_n

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Moment of Inertia I

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Shaft Stiffness k

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Operating Speed Margin

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Second Moment of Area

Central Mass — Simply Supported

For a shaft with a concentrated mass m at mid-span and simply supported ends:

Support Condition Factors

The stiffness coefficient k changes with support type:

Support	Stiffness k	Factor vs SS
Simply Supported (central load)	48EI / L³	1.00
Fixed-Fixed (central load)	192EI / L³	4.00
Cantilever (end load)	3EI / L³	0.0625

Practical Example

Example — Pump Shaft

Given: L = 800 mm, d = 50 mm, m = 30 kg, Steel E = 210 GPa, Simply Supported

I = π × 50⁴ / 64 = 306,796 mm⁴

k = 48 × 210,000 × 306,796 / 800³ = 6,029 N/mm

ω_n = √(6,029,000 / 30) = 448.2 rad/s

N_cr = 448.2 × 60 / (2π) = 4,280 RPM

⚠️ Note: This simplified model assumes a massless shaft with a single concentrated mass. For more accurate results on heavy shafts, consider the Rayleigh or Dunkerley methods that account for distributed shaft mass.

Rotor Critical Speed Calculator | Shaft Natural Frequency

Published by Nikolai Shelkovenko on February 15, 2026 February 15, 2026

Results

Second Moment of Area

Central Mass — Simply Supported

Support Condition Factors

Practical Example