Critical speed
In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity which excites the natural frequency of a rotating object, such as a shaft, propeller, leadscrew, or gear. As the speed of rotation approaches the object's natural frequency, the object begins to resonate which dramatically increases systemic vibration. The resulting resonance occurs regardless of orientation.
When the rotational speed is equal to the numerical value of the natural vibration then that speed is called critical speed.
Critical speed of shafts
All rotating shaft, even in the absence of external laod, deflect during rotation. The combined weight of a shaft and wheel can cause deflection that will create resonant vibration at certain speeds, known as Critical Speed. The magnitude of deflection depends upon the followings :- (a) stiffness of the shaft and it’s support (b) total mass of shaft and attached parts (c) unbalance of the mass with respect to the axis of rotation (d) the amount of damping in the system Therefore, the calculation of critical speed for fan shaft is necessary.
Critical Speed Equation (Nc)
There are two method used to calculate critical speed, Rayleigh-Ritz and Dunkerley Equation. Both the Rayleigh-Ritz and Dunkerley equation are an approximations to the first natural frequency of vibration, which is assumed to be nearly equal to the critical speed of rotation. In general, the Rayleigh-Ritz equation overestimates and the Dunkerley equation underestimates the natural frequency. The equation illustrated below is the Rayleigh-Ritz equation, good practice suggests that the maximum operation speed should not exceed 75% of the critical speed.
Criticalspeed,Nc =30/π *(suare root of g/δst)
where : g = gravity acceleration (9.81 m/s2) δst = total maximum static deflection
Critical speed depend upon the magnitude or location of the load or load carried by the shaft, the length of the shaft, its diameter and the kind of bearing support.
