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EXPT NO: NAME:
DATE: ROLL NO:
WHIRLING OF SHAFT
AIM
To study the whirling phenomenon of the given shafts and to
compare the theoretical and
experimental values of critical speeds of whirling.
APPARATUS
Apparatus consists of a frame to support the driving motor with
speed control unit to vary the
speed and two bearing blocks and to support the holding chuck.
Chuck supports the free end of
the shaft. Shafts of different diameters (d1, d2, and d3),
tachometer, Vernier calipers and spanner
are also needed.
THEORY AND PRINCIPLE
When a shaft rotates it will go into transverse oscillations if
the shaft is out of balance due to
eccentricity of CG and neutral axis of the shaft, e. The
resulting centrifugal force will induce
the shaft to vibrate. When shaft rotates at speed equal to
natural frequency of transverse
oscillations this vibration becomes large and shows up as
whirling of shaft. It also occurs at
multiples of resonant speed.
a- Mode 1
b- Mode 2
c- Mode 3
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When the shaft of mass M rotates, the centrifugal force will
force it to bend out. Let the
deflection of the shaft due to centrifugal force be r. The
distance of CG is then r+e. Let the
shaft rotates at rad/s and trasverse stiffness of the shaft be
Kt .
The centrifugal force is M2(r+e)
Equating force we have Kt r = M2(r+e)
Kt/M=n, so r = e / (1-(/n)2)
If =n then r = infinity. So the shaft will whirl at its natural
frequency.
PROCEDURE
1. The given rod is held between holding chuck and bearing.
2. The motor is switched on and speed is to be increased to
certain value at which violent
vibration of rod occurs.
3. The shaft deflects like a single bow or like a skipping
rope.
4. The speed is measured with tachometer.
5. The speed is increased further to a value at which double bow
is formed.
6. This speed is also measured and above procedure is repeated
for three different shaft
diameters.
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TABULAR COLUMN
Sl
No
Diameter
of shaft
(m)
Area of
shaft
(m2)
M.I. of
shaft
(m4)
UDL
(N/m)
Static
deflection
(m)
Mode Theoretical
critical
speed
Actual
critical
speed
1
2
1
2
1
2
OBSERVATIONS AND SAMPLE CALCULATIONS FOR SET NO:__________
d- diameter of the shaft= m
A -Cross section area of the shaft, (/4) d2= = m2
- density of the shaft material= 8000 Kg/m3
g- acceleration due to gravity= 9.81 m/s
W - uniformly distributed load on the shaft, g A= N/m
Static deflection of the shaft (both ends fixed) due to self
weight is given by
= 1/384 (WL4/EI) m
L length of the shaft = m
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E Youngs modulus of the shaft= 2.1 x 1011 N/m2
I - Moment of inertia of the shaft about the horizontal,
(/64) d4= = m4
The lowest critical speed is:
Theoretical critical speed at node 1 = = rpm
Theoretical critical speed at node 2 = = rpm
RESULTS
The experiment on whirling of shaft is done and following
results are obtained.
For shaft 1 (d = m);
Theoretical critical speed at node 1 =________rpm
Theoretical critical speed at node 2 =________rpm
Experimental critical speed at node 1= ________rpm
Experimental critical speed at node 2= ________rpm
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For shaft 2 (d = m);
Theoretical critical speed at node 1 =________rpm
Theoretical critical speed at node 2 =________rpm
Experimental critical speed at node 1= ________rpm
Experimental critical speed at node 2= ________rpm
For shaft 3 (d = m);
Theoretical critical speed at node 1 =________rpm
Theoretical critical speed at node 2 =________rpm
Experimental critical speed at node 1= ________rpm
Experimental critical speed at node 2= ________rpm
INFERENCE
