14-01-2014, 04:37 PM
WHIRLING OF SHAFT APPARATUS
Aim:
To determine theoretically the critical speed of the given shaft with the given end conditions
Description:
The speed at which the shaft runs so that additional deflection of the shaft from the axis of
rotation becomes infinite is known as critical speed.
Normally the centre of gravity of a loaded shaft will always displace from the axis of rotation
although the amount of displacement may be very small. As a result of this displacement, the centre
of gravity is subjected to a centripetal acceleration as soon as the Shaft begins to rotate. The inertia
force acts radially outwards and bend the shaft. The bending of shaft not only depends upon the value
of eccentricity, but also depends upon the speed at which the shaft rotates.
Formula used:
fn = K√(EgI/wl4) and Nc = fn X 60
Where, fn= natural frequency of vibration in Hz
g = acceleration due to gravity, (9.81m/s2), E= modules of elasticity of the shaft
I = moment of inertia of shaft in m4, w= weight /unit length in N/m
L = effective length of the shaft between supports in m. and N= speed of the shaft in RPM
K = constant (2.45)
Calculation:
1. Moment of inertia
2. Weight of solid shaft
3. Natural frequency
4. Critical speed