critical speed.pdf

1-5 Technical Bulletin TBN017.0/1998 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. st g30 Nc,speedCritical δπ = 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. Total Maximum Static Deflection (δst) The maximum static deflection, δst, is obtained by adding both the maximum static deflection of the rotating shaft and the load. (1) Maximum static deflection on shaft (δstI) 1.1) EI384 wL5 Ist 3 =δ 2-5 1.2) EI8 wL Ist 3 =δ (2) Maximum static deflection on load only (δst2) 2.1 ) EI48 WL 2st 3 =δ 2.2 )