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

Single disk on a flexible shaft: ω_n = √(k/m), unbalance response, whirl orbit, phase lag, and critical-speed crossing.

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

About this model

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

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.

Continue with similar topics in this category — or all 48 in Engineering.

View category →

NewUniversity / research

Vibration Isolation Transmissibility

Launch Simulator

SDOF base-excitation isolator: transmissibility T(r,ζ), resonance peak, phase lag, and the isolation region above r = √2.

NewUniversity / research

Torsional Drivetrain Resonance

Launch Simulator

Two-inertia torsional drivetrain: shaft stiffness and damping, twist angle, first natural mode, resonance response, and optional backlash deadzone.

NewUniversity / research

Euler Column Buckling

Launch Simulator

Elastic column stability with P_cr = π²EI/(KL)²: choose end conditions, effective length factor K, first mode shape, and load ratio P/P_cr.

NewUniversity / research

Bode & Nyquist from Pole–Zero Map

Launch Simulator

Click the s-plane to place real or complex-conjugate poles (●) and zeros (×); G(s)=K∏(s−z)/∏(s−p). Live Bode magnitude/phase and Nyquist plot with −1 point; phase and gain margins from principal crossings (teaching heuristics).

NewSchool

Stepper Motor (4-phase)

Launch Simulator

Full-step vs half-step commutation; rotor snaps as coils A–B–A′–B′ sequence.

NewSchool

Planetary Gear Set

Launch Simulator

Sun, planets, internal ring: Willis equation, hold Sun/ring/carrier and compare speed ratios.

Jeffcott Rotor Critical Speed

Live graphs

About this model

How it works

Key equations

Frequently asked questions

Related simulators

Vibration Isolation Transmissibility

Torsional Drivetrain Resonance

Euler Column Buckling

Bode & Nyquist from Pole–Zero Map

Stepper Motor (4-phase)

Planetary Gear Set

Jeffcott Rotor Critical Speed

Live graphs

About this model

How it works

Key equations

Frequently asked questions