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Bilal

This experiment aims to determine the whirling speed of a loaded shaft and verify Dunkerley's equation. Dunkerley's equation calculates the critical frequency of a system with multiple attached disks based on the individual critical frequencies of each disk and the shaft alone. The experiment involves measuring the critical frequencies of a shaft loaded with 1, 2, or 3 disks individually, as well as with all disks attached. The measured frequencies are then used to verify that they satisfy Dunkerley's equation.

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116 views3 pages

Bilal

This experiment aims to determine the whirling speed of a loaded shaft and verify Dunkerley's equation. Dunkerley's equation calculates the critical frequency of a system with multiple attached disks based on the individual critical frequencies of each disk and the shaft alone. The experiment involves measuring the critical frequencies of a shaft loaded with 1, 2, or 3 disks individually, as well as with all disks attached. The measured frequencies are then used to verify that they satisfy Dunkerley's equation.

Uploaded by

bilal farid
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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EXPERIMENT 14

OBJECTIVE:
To determine the whirling speed of loaded shaft and verify Dunkerley‟s equation.

APPARATUS:
Whirling of Shaft Apparatus

THEORY:
At certain speed a rotating shaft or rotor exhibits excessive transverse vibrations. The angular
velocity of the shaft at which this occurs is called a critical/whirling speed of shaft.

When a shaft rotates it may well go into transverse oscillations; if the shaft is out of balance, the
resulting centrifugal force will induce the shaft to vibrate. When the shaft rotates at the speed equal to
the natural frequency of transverse oscillations, this vibration becomes large and shows up as whirling
of the shaft.

If the first whirling speed is maintained then the resulting amplitude becomes sufficient to cause
buckling and failure. However, if the speed is rapidly increased before such effects occur, then the
shaft is seen to re-stabilize and run true again until another specific speed is encountered where a
double bow is produced as shown in Figure-1. The second speed is called Second Critical Speed.
For a shaft loaded with a number of disks as shown in Figure; the first critical frequency for the
system can be found from Dunkerley's Equation as follows:

Where:
f = critical frequency of the system as a whole (Hz)
fs = critical frequency of the shaft alone (Hz)
f1, f2 , f3 = critical frequency of the attached disks 1,2,3 individually without the effect of other masses

PROCEDURE:

1) Attach a shaft of known diameter (7mm) and length (865mm) to the apparatus.
2) Select the shaft end conditions as required.
3) Attach the first disk (400g) midway between the two supports.
4) Switch on the speed control unit and adjust the speed carefully until you obtain whirling
condition. Record the whirling frequency of the system f.
5) Calculate the critical frequency for the first disk alone, f1 , from the following equation:

Where fs is the whirling frequency for the shaft alone in the simply-supported configuration
and can be taken from previous experiment.

6) Remove the first disk and attach second disk (300g) at 0.25L from the motor-side support and
repeat the above procedure to calculate f2 for the second disk alon
7) Attach the third disk (300g) alone at 0.75L from the motor-
side support and repeat the procedure to calculate f3 for the
third disk alone.

8) Attach all the three disks at their respective positions and run the DC
motor to find the critical frequency for the combination and verify that
the Dunkerley‟s equation is satisfied.

in Hz (as in Hz (from f i in Hz
Sr. No. Loading measured) previous exp.) i =1, 2, 3
1 First disk only

2 Second disk only

3 Third disk only

4 All disks

PRECAUTIONS:

1. Keep the shaft covered with its plastic case during operation.
2. Pass through the critical speed quickly.

COMMENTS:

1. Shaft end conditions are not as exact as assumed in theory.


2. Exact material properties of the shaft are not known.
3. Barriers restrict the motion of shaft; so we can‟t increase the speed beyond a
specific limit.

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