What is the critical speed of a shaft and why is it important?

Critical speed is the rotational speed at which a shaft's natural frequency of lateral vibration equals the rotation frequency, causing resonance with potentially destructive amplitudes. Calculated as Nc = 30/pi x sqrt(g/delta_static) RPM for simple cases, or using Rayleigh-Ritz method for complex systems. Operating speed should be at least 20% away from critical speed. Rigid rotors operate below first critical, flexible rotors (like turbines) operate above. Critical speed increases with stiffness and decreases with mass.