Why does vibration peak near critical speed?

At r = Ω/ω_n near 1, the forcing frequency from imbalance matches the lateral natural frequency of the rotor. Damping limits the peak but does not remove the resonance.

Is it always unsafe to run above a critical speed?

Not necessarily. Many machines pass through a critical speed during startup and operate supercritically. The design question is whether the crossing and operating range satisfy vibration and bearing-load limits.

Jeffcott Rotor Critical Speed

The Jeffcott rotor is the classic first model of rotor dynamics: a rigid disk of mass m mounted on a massless flexible shaft with lateral stiffness k and damping ratio ζ. Its first critical speed is ω_n = sqrt(k/m). A small mass eccentricity e creates a rotating unbalance force m e Ω²; the steady orbit amplitude follows X/e = r² / sqrt((1−r²)² + (2ζr)²), where r = Ω/ω_n. This simulator animates the disk whirl, plots amplification versus speed ratio, and highlights the passage through the first critical speed. It is a teaching model only: real rotors include bearings, gyroscopic effects, shaft distributed mass, anisotropic stiffness, multiple modes, seals, rubs, thermal bow, and nonlinear supports.

Who it's for: Rotor dynamics, machine vibration, turbomachinery, pumps, motors, and mechanical design introductions.

Key terms

Jeffcott rotor
Critical speed
Unbalance response
Whirl orbit
Damping ratio

The response peaks near the first critical speed. In practice rotors are balanced, accelerated through critical speeds with care, and checked against bearing loads, mode shapes, and vibration limits.

Live graphs

How it works

Jeffcott rotor critical-speed simulator: disk on a flexible shaft with unbalance force, resonance amplification, whirl orbit, phase lag, and critical speed crossing.

Key equations

ω_n = sqrt(k/m), r = Ω/ω_n

X/e = r² / sqrt((1−r²)² + (2ζr)²)

Frequently asked questions

Why does vibration peak near critical speed?: At r = Ω/ω_n near 1, the forcing frequency from imbalance matches the lateral natural frequency of the rotor. Damping limits the peak but does not remove the resonance.
Is it always unsafe to run above a critical speed?: Not necessarily. Many machines pass through a critical speed during startup and operate supercritically. The design question is whether the crossing and operating range satisfy vibration and bearing-load limits.

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Live graphs

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Key equations

Frequently asked questions

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Key equations

Frequently asked questions