What is critical speed in a rotating shaft?

Critical speed is the rotational speed at which a shaft becomes unstable and begins to vibrate violently (whirl) due to resonance with its natural frequency.

What formula does this calculator use?

It uses the single-DOF rotor model where angular frequency is ω_n = √(k/m) rad/s, natural frequency is f_n = ω_n / 2π Hz, and critical speed is n_cr = (60/2π)·ω_n RPM.

Can I calculate multiple critical speeds for multi-mass systems?

No, this calculator uses a single-degree-of-freedom model, which calculates the primary (first) critical speed for a single concentrated mass.

What units should I use for stiffness and mass?

Use Newtons per meter (N/m) for stiffness (k) and kilograms (kg) for mass (m).

How do I prevent a shaft from operating at critical speed?

You can change the operating speed, increase shaft stiffness (e.g., by increasing diameter or shortening span), or reduce the rotor mass.

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Shaft Critical Speed Calculator

Calculate the critical (resonance) speed of a rotating shaft using the single-DOF rotor model. ω_n = √(k/m), n_cr = (60/2π)·√(k/m) rpm. Also returns the natural frequency f_n in Hz.

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1 examples

k = 200000 N/m, m = 5 kg

ω_n = √(40000) = 200 rad/s. f_n = 200/(2π) ≈ 31.8310 Hz. n_cr = 60·200/(2π) ≈ 1909.8593 rpm.

{"result":"Critical speed: ω_n = √(k/m) = √(200000/5) = 200.0000 rad/s. f_n = 31.8310 Hz. n_cr = (60/2π)·ω_n = 1909.8593 rpm.","metadata":{"input":{"stiffness":200000,"mass":5},"result":{"naturalFrequency":31.831,"naturalFrequencyUnit":"Hz","angularFrequency":200,"angularFrequencyUnit":"rad/s","criticalSpeed":1909.8593,"criticalSpeedUnit":"rpm"}}}

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SettingsAdjust formats, ranges, numbers, and modes.3

Stiffness k (N/m)numberRequiredMass m (kg)numberRequiredDecimal PlacesnumberOptional

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Shaft Critical Speed Calculator

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Examples

1. Verifying a Small Fan Rotor Shaft

2. Analyzing a Heavy Industrial Rotor

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