LAB 10 Whirling Speed of Shaft
Experiment 09
Objective
To investigate the critical speed of a shaft loaded with a mass at the center of the shaft
Apparatus
Fig. 9- a: Critical Speed Investigation Apparatus
1 Switch Box 2 Drive Motor
3 Inductive Speed Sensor 4 Flexible Coupling
5 Mass Disc 6 Elastic Shaft
7 Protective Cover 8 Safety Bearing
9 Self-Aligning Ball Bearing
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LAB 10 Whirling Speed of Shaft
Theoretical Background
Simply supported beam:
A beam supported on the ends which are free to rotate and have no moment resistance is known
as a simply supported beam. A Typical simply supported beam has two supports, one at each end.
In the below-given figure, one end is pinned supported and the other is roller support.
Figure 1: simple supported beam
Moment of inertia:
Moment of inertia is defined as the quantity expressed by the body resisting angular acceleration
which is the sum of the product of the mass of every particle with its square of a distance from
the axis of rotation.
Critical speed:
Critical speed is the rotational speed at which dynamic acting forces cause a machine component to vibrate
at its inherent frequency and can even result in resonance vibrations across the entire machine and pump
set.
The whirling speed, also known as the crucial speed of a shaft, is the speed at which a spinning shaft begins
to vibrate forcefully in the transverse direction when rotated horizontally. In other words, the critical speed,
also known as the whirling speed, is the speed at which resonance occurs. As a result, when the natural
frequency of transverse vibration meets the frequency of a rotating shaft, shaft whirling occurs.
The critical or whirling speed is the speed at which the shaft moves at which the excess deviation of the
shaft is eliminated.
Causes of the Critical Speed:
The critical speed may occur due to one or more of the following reasons:
Eccentric mountings like gears, flywheels, pulleys, etc.
Bending of the shaft due to its own weight
Non-uniform distribution of rotor material.
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LAB 10 Whirling Speed of Shaft
Resonance:
A phenomenon in which an external force or a vibrating system forces another system around it to vibrate
with greater amplitude at a specified frequency of operation.
Example:
Soldiers parading on the bridge are frequently requested to stop because their rhythmic marching might
generate significant vibrations at the bridge's inherent frequency. If the synchronized footfall resonate with
the bridge's inherent frequency, the bridge may collapse. One example is the Tacoma Bridge Collapse, in
which the frequency of the air matched the frequency of the bridge, resulting in its disintegration.
Formula for calculating the theoretical critical speed.
3𝐸𝐼
𝑁=√ 3
𝑚𝑙
𝜋𝑑4
𝐼=( )
64
𝐸𝐼
𝐶 = (48 )
𝐿3
Experimental Procedure
1. Set speed potentiometer 1 on switchbox to zero
2. Set switch for speed adjustment to potentiometer 1
3. Switch on motor. Run up rotor very slowly with potentiometer 1
4. As soon as rotor contacts safety bearing (hard running noise), read speed n u off speed
counter and record
5. Reduce speed again
6. Set speed with potentiometer 2 which is guaranteed to lie above critical speed (3pprox..
500 rpm above speed nu
7. Switch specified speed on potentiometer 2
8. Now accelerate rotor as quickly as possible and run through resonance point
9. If resonance point is not overcome, switch back to potentiometer 1 and increase speed on
potentiometer 2
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LAB 10 Whirling Speed of Shaft
10. Now lower speed slowly with potentiometer 2 in over-critical range until rotor is near
resonance point and contacts safety bearing
11. Read off speed no and record. The resonance speed results as the mean value from the two
speeds nu and no
𝑛𝑢 + 𝑛𝑜
𝑛𝑐𝑟𝑖𝑡 =
2
Observations and Calculation
Critical
Speed from Speed from Experimental
Distance between Speed
Sr. # below 𝒏𝒖 in above 𝒏𝒖 in Critical Speed
bearings L in mm calculated
rpm rpm 𝒏𝒄𝒓𝒊𝒕 in rpm
𝒏𝒄𝒓𝒊𝒕 in rpm
1 450 756 784 770 801
2 350 1751 1821 1786 1167
3 320 1691 1764 1726 1335
4 300 1642 1771 1708 1471
5 425 811 831 821 815
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LAB 10 Whirling Speed of Shaft
Specimen Calculation
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LAB 10 Whirling Speed of Shaft
Discussion:
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