Critical Speed Calculator
A shaft whirls when it turns at its natural frequency √(g/δ): a 0.5 mm static deflection gives a critical speed of 1337.58 rpm.
1337.58344067068 rpm
Full answer, then cut to fewer decimals (not rounded):
- 1337.58344067068 rpm
- 1337.5834406706 rpm
- 1337.583440670 rpm
- 1337.58344067 rpm
- 1337.5834406 rpm
- 1337.583440 rpm
- 1337.58344 rpm
- 1337.5834 rpm
- 1337.583 rpm
- 1337.58 rpm
- 1337.5 rpm
- Critical angular speed ωc
- 140.071 rad/s
- Critical frequency
- 22.2931 Hz
Step-by-step solution
- ωc = √(g/δ) = √(9.81 ÷ 0.0005) = 140.071 rad/s
- Nc = 60ωc/2π = 1337.58 rpm
Critical Speed Formula
ωc = √(g/δ) = √(k/m), Nc = 60ωc/2π
δ static deflection under the rotor, g = 9.81 m/s²
Worked Example
A rotor whose weight deflects the shaft 0.5 mm:
- ωc = √(g/δ) = √(9.81 ÷ 0.0005) = 140.071 rad/s
- Nc = 60ωc/2π = 1337.58 rpm
Critical frequency: 22.2931 Hz
More Theory of Machines and Vibrations Calculators
-
Natural Frequency Calculator
ωn = √(k/m), fn = ωn/2π, ζ = c/2√(km)
m mass, k stiffness, c damping coefficient
Example: A 10 kg mass on a 4000 N/m spring: Natural frequency fn = 3.1831 Hz.
-
Transmissibility Calculator
TR = √[1 + (2ζr)²] ÷ √[(1 − r²)² + (2ζr)²]
r = ω/ωn frequency ratio, ζ damping ratio
Example: A machine running at twice the natural frequency with ζ = 0.1: Transmissibility TR = 0.355862.
-
Gear Train Calculator
N₁/Nout = Π driven teeth ÷ Π driving teeth
train value = 1/speed ratio
Example: A compound train 20/60 then 15/45 driven at 1200 rpm: Output speed N = 133.333 rpm.
-
Flywheel Calculator
ΔE = I ω² Cs = m k² ω² Cs
Cs = (ωmax − ωmin)/ω, k radius of gyration
Example: ΔE = 5000 J at 600 rpm with Cs = 2 % and k = 0.5 m: Moment of inertia I = 63.3257 kg·m².
Frequently asked questions
Is critical speed the same as natural frequency?
Yes: the shaft whirls violently when its rotational speed equals the natural frequency of transverse vibration.
How do I handle several discs on one shaft?
Use Dunkerley’s method, 1/ωc² = Σ 1/ωᵢ², or the Rayleigh energy method with each disc’s deflection.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Critical Speed Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/critical-speed-calculator/
IEEE
Scientific Converters, "Critical Speed Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/critical-speed-calculator/