What is critical speed?

Critical speed is the rotational speed at which a shaft's rotational frequency equals one of its natural bending frequencies, causing resonance. At critical speed, even small unbalance produces large vibrations that can damage bearings, seals, and the shaft itself.

Why avoid operating near critical speed?

Operating near critical speed amplifies vibrations exponentially due to resonance. The standard practice is to operate at least 20–30% below or above the critical speed. The region within ±20% of critical speed is called the critical speed band and should be avoided.

How to raise critical speed?

Critical speed can be raised by increasing shaft diameter (raises stiffness by d⁴), using a stiffer material (higher E modulus), reducing shaft length, reducing rotor mass, or changing support conditions from simply supported to fixed-fixed.

What is the difference between rigid and flexible rotor?

A rigid rotor operates well below its first critical speed (typically below 70% of Ncr). A flexible rotor operates above its first critical speed and must pass through resonance during run-up and coast-down. Flexible rotors require more careful balancing.

What safety margin is recommended?

API 610 and API 617 recommend that the first critical speed be at least 20% above the maximum continuous operating speed (for rigid rotors) or that operating speed be at least 15–20% above the critical speed (for flexible rotors passing through resonance).

Herramienta de Ingeniería Gratuita — #009

Calculadora de velocidad crítica del rotor

Calcule la primera velocidad crítica (frecuencia natural) de un eje con masa central o masa distribuida utilizando el método de Rayleigh. Compare con las RPM de operación para el margen de seguridad.

Masa Central Método de Rayleigh 3 Tipos de Soporte

Longitud del Eje L (mm)

Diámetro del Eje d (mm)

Masa del Rotor m (kg)

Material (Módulo E)

Tipo de soporte

Velocidad de funcionamiento (RPM, opcional)

Preajustes rápidos

Resultados

Velocidad Crítica (Masa Central)

—

Frecuencia natural

—

Frecuencia Angular ω_n

—

Momento de inercia I

—

Rigidez del Eje k

—

Margen de Velocidad de Operación

—

Momento de Inercia de Área

Masa Central — Apoyos Simples

Para un eje con una masa concentrada m en el punto medio y extremos con apoyos simples:

Factores de Condición de Soporte

El coeficiente de rigidez k cambia con el tipo de soporte:

Soporte	Rigidez k	Factor vs AS
Apoyos Simples (carga central)	48EI / L³	1.00
Empotrado-Empotrado (carga central)	192EI / L³	4.00
Cantilever (carga en el extremo)	3EI / L³	0.0625

Ejemplo práctico

Ejemplo — Eje de Bomba

Datos: L = 800 mm, d = 50 mm, m = 30 kg, Acero E = 210 GPa, Apoyos Simples

I = π × 50⁴ / 64 = 306,796 mm⁴

k = 48 × 210,000 × 306,796 / 800³ = 6,040 N/mm

ω_n = √(6,040,000 / 30) = 448.7 rad/s

N_cr = 448.7 × 60 / (2π) = 4,285 RPM

⚠️ Nota: Este modelo simplificado asume un eje sin masa con una sola masa concentrada. Para obtener resultados más precisos en ejes pesados, considere los métodos de Rayleigh o Dunkerley que tienen en cuenta la masa distribuida del eje.