Glossary term

Critical Speed

Rotational speed at which a running excitation order strongly couples with a rotor or structural mode and can produce large vibration.

Branch: Mechanical Engineering
Glossary type: quantity
Content: Glossary term
Updated: Jun 25, 2026
Revision: v1.0.1 · reviewed

Definition

quantity

Critical speed is a rotational speed at which a rotor, shaft, support or coupled machine mode is strongly excited by a running excitation order.

A critical speed occurs when running speed, or one of its harmonics or orders, coincides with a natural frequency or damped rotor mode strongly enough to create high vibration. In rotor dynamics, critical speeds depend on rotor mass and stiffness, bearings, seals, supports, damping, gyroscopic effects, unbalance, operating condition and whether the mode is forward, backward, bending or torsional.

Critical speed is a rotational speed where a running excitation order strongly excites a rotor, shaft, support or coupled machine mode. It is often associated with rotor bending modes, but the same screening logic also applies to torsional modes, frame modes, foundation modes and coupled drivetrain modes.

For a running speed $n$ in revolutions per minute, the one-per-revolution excitation frequency is:

\displaystyle f_{1x}=\frac{n}{60}

For excitation order $m$ , such as 2x, gear mesh order or blade-passing order:

\displaystyle f_{exc}=m\frac{n}{60}

If a mode has frequency $f_r$ , the speed at which order $m$ crosses that mode is:

\displaystyle n_{crit}=\frac{60f_r}{m}

A common separation measure is:

\displaystyle M_{sep}=\frac{|n_{run}-n_{crit}|}{n_{crit}}

Some standards and companies use a denominator based on running speed or excitation frequency instead. The convention must be stated because the numerical percentage changes.

Engineering Role

Critical-speed review helps engineers decide whether a machine can run continuously at a speed, pass through a speed during startup, or needs an avoidance band. It is central to pumps, fans, compressors, turbines, motors, generators, spindles, propeller shafts, gearboxes and high-speed test rigs.

Critical speeds are not automatically forbidden. Many machines accelerate through one or more critical speeds safely if damping is sufficient, the ramp is controlled, vibration limits are enforced and dwell time near resonance is short. Continuous operation near a lightly damped critical speed is more severe because vibration cycles accumulate and can damage bearings, seals, couplings, supports or fatigue-sensitive details.

Rotor critical speeds can shift with bearing stiffness, temperature, preload, seal forces, foundation flexibility, gyroscopic effects, fluid loading, added mass, balance state and operating load. A speed that is safe on a shop test stand may not be safe after installation on a flexible skid, ship foundation or piping-connected package.

Damping, Avoidance Bands and Release Evidence

The severity of a critical-speed crossing depends on response, not the crossing speed alone. For a simplified single-mode screen, the frequency ratio is:

\displaystyle r=\frac{f_{exc}}{f_r}

and a linear dynamic amplification factor can be written as:

\displaystyle D(r,\zeta)=\frac{1}{\sqrt{(1-r^2)^2+(2\zeta r)^2}}

where $\zeta$ is damping ratio. This is not a complete rotor-dynamic model, but it explains why two machines with the same separation margin can behave differently: the lightly damped machine amplifies much more near $r=1$ .

When a speed must be avoided, engineers usually define a band rather than a single number:

n_{low}\leq n \leq n_{high}

If a run-up crosses that band at ramp rate $\dot{n}$ , the exposure time is:

\displaystyle t_{band}=\frac{n_{high}-n_{low}}{\dot{n}}

A short controlled pass-through with trip protection may be acceptable where continuous operation is not. A release package should therefore state the operating speed range, forbidden or limited bands, acceleration and coast-down procedure, vibration trip levels, damping evidence, balance state, bearing condition and what happens if the controller dwells near the crossing.

Measured evidence is the deciding layer. Useful evidence includes amplitude and phase versus speed, order-tracked 1x or higher-order response, waterfall spectra, orbit plots, bearing temperature, proximity-probe runout checks, repeat run-up and coast-down comparisons, and uncertainty in the model-to-test correlation.

Worked Example: Speed Crossing and Separation Margin

A variable-speed fan operates from:

900\ \text{rpm} \leq n \leq 1800\ \text{rpm}

A run-up test and finite element review identify a bending-like mode at:

f_r=27\ \text{Hz}

For a 1x unbalance excitation, $m=1$ , so the critical speed is:

\displaystyle n_{crit}=\frac{60(27)}{1}=1620\ \text{rpm}

The critical speed lies inside the operating range. If normal operation is planned at:

n_{run}=1785\ \text{rpm}

the separation from the 1x critical speed is:

\displaystyle M_{sep}=\frac{|1785-1620|}{1620}=0.102=10.2\%

Now check a 2x excitation against a support or local mode at:

f_r=60\ \text{Hz}

For $m=2$ :

\displaystyle n_{crit}=\frac{60(60)}{2}=1800\ \text{rpm}

That crossing occurs at the top of the operating range, so a speed limit, avoidance band, damping review or structural modification may be required.

Engineering comment: the 1785 rpm point is above the first 1x critical speed, but the machine still crosses 1620 rpm during startup and coast-down. The 2x crossing at 1800 rpm is even closer to the intended upper operating limit. A release decision should use measured vibration amplitude and phase, damping, ramp rate, duty cycle, bearing loads, fatigue sensitivity and trip limits, not separation percentage alone.

Critical speed is not natural frequency by itself. Natural frequency is a modal frequency. Critical speed is the rotational speed at which a running order intersects that modal frequency.

Critical speed is not generic resonance. Resonance is the response amplification condition; critical speed is the rotating-machine speed associated with that condition.

Critical speed is not always the shaft speed equal to one mode frequency. Higher orders, blade passing, gear mesh, electrical forcing, torsional orders and subsynchronous components can create critical crossings at different running speeds.

Critical speed is not automatically a failure speed. With sufficient damping, fast crossing and acceptable amplitude, a machine may safely pass through a critical speed. Continuous operation near a critical speed needs stronger evidence.

Critical speed is not fixed for all installations. Bearing, support, seal, fluid and foundation changes can move the critical speed.

Validation and Common Mistakes

A defensible critical-speed assessment states the rotor configuration, bearing and support data, operating speed range, excitation orders, predicted and measured modes, damping estimates, unbalance state, run-up or coast-down evidence, vibration limits, separation convention, ramp procedure and uncertainty.

Common mistakes include:

checking only 1x speed and ignoring 2x, blade-passing, gear-mesh or torsional orders;
using a free-free shaft natural frequency when the installed bearings and supports control the mode;
treating a shop-test critical speed as unchanged after installation;
focusing on steady speed while ignoring startup and coast-down crossings;
applying one generic separation percentage without considering damping, consequence and uncertainty;
balancing a rotor without checking whether a high response is actually a critical-speed crossing;
accepting a speed range without measured amplitude, phase or order-tracked evidence.

REF

Disciplines

Critical Speed

Definition

Engineering Role

Damping, Avoidance Bands and Release Evidence

Worked Example: Speed Crossing and Separation Margin

Validation and Common Mistakes

See also

Engineering Role

Damping, Avoidance Bands and Release Evidence

Worked Example: Speed Crossing and Separation Margin

Distinction from Related Terms

Validation and Common Mistakes