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Critical speed is the rotational speed at which a shaft's rotational frequency matches one of its natural bending frequencies, causing resonance. At critical speed, even tiny unbalance forces are amplified dramatically, leading to dangerous vibration levels.

Every rotating shaft has one or more critical speeds. The first (lowest) critical speed is the most important for design purposes.

Operating near critical speed causes:

• Exponential amplification of vibration from unbalance
• Excessive bearing loads and premature failure
• Shaft deflection beyond elastic limits
• Seal damage and oil leakage
• Risk of catastrophic shaft failure

The industry standard is to maintain at least a 20% margin between operating speed and any critical speed.

Critical speed can be increased by:

• Increasing shaft diameter — stiffness scales with d⁴, very effective
• Reducing shaft length — stiffness scales with 1/L³
• Using stiffer material — higher E modulus
• Reducing rotor mass — lighter rotor = higher frequency
• Changing supports — fixed-fixed is 4× stiffer than simply supported

A rigid rotor operates well below its first critical speed (N_op < 0.7 × N_cr). It can be balanced at low speed in a balancing machine.

A flexible rotor operates above its first critical speed and must pass through resonance during startup. It requires high-speed balancing and may need modal balancing at multiple speeds.

Common standards recommend:

• API 610/617: First critical speed ≥ 120% of max continuous speed (rigid rotors)
• API 612: Operating speed ≥ 115% above first critical (flexible rotors)
• General practice: Stay at least 20–30% away from any critical speed

The ±20% band around a critical speed is considered the danger zone and should be avoided during continuous operation.