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Whirling speed of the shaft is the speed at which

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MPPSC AE Mechanical 2021 Official Paper
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  1. Shaft tends to vibrate in longitudinal direction
  2. Torsional vibrations occur
  3. Shaft tends to vibrate vigorously in transverse direction
  4. Combination of transverse and longitudinal vibration occurs

Answer (Detailed Solution Below)

Option 3 : Shaft tends to vibrate vigorously in transverse direction
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Detailed Solution

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Explanation:

Critical or whirling speed of the shaft

Whirling speed or Critical speed of a shaft is defined as the speed at which a rotating shaft will tend to vibrate violently in the transverse direction if the shaft rotates in the horizontal direction. In other words, the whirling or critical speed is the speed at which resonance occurs.

Additional Information

  • When the natural frequency of the system coincides with the external forcing frequency, it is called resonance.
  • The speeds at which resonance occurs are known as the critical speeds/ whirling speeds or whipping. At this speed, the shaft runs so that the deflection of the shaft from the axis of rotation becomes infinite and the shaft tends to vibrate violently in the transverse direction.
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Q2.The whirling speed of a rotating shaft depends on its _________.
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Q4.If two nodes are noticed at a frequency of 1800 rpm during whirling of a simply supported long slender rotating shaft, determine the first critical speed of the shaft (in rpm).
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Q1.At a certain speed, revolving shafts tend to vibrate violently in transverse direction. This speed is known as
Q2.A cantilever beam of cross section area 'A', moment of Inertia 'T' and length 'L' is having natural frequency ω1. If the beam is accidently broken into two halves, the natural frequency of the remaining cantilever beam ω2 will be such that
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Q5.Consider a uniform shaft of length L fixed at its upper end and carrying a disc of the moment of inertia I at its lower end. The disc is twisted about the vertical axis and released. 'fa' is the natural frequency of the system when the shaft is assumed as massless, and 'fb' is the natural frequency of the system when the shaft is considered of the same moment of inertia as that of the disc. Find the ratio fa/fb.
Q6.A spring-mass system consists of a mass of 5 kg and two springs of stiffness 8 N/mm and 12 N/mm. The system is arranged in different manners, that is: (i) the mass is suspended at the bottom of two springs in series, and (ii) the mass is fixed between two springs. The ratio of natural frequencies of the case (ii) to those of case (i) is approximately ___________. 
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Q10.A shaft which is 50 mm diameter and 3 metres long is simply supported at the ends and carries three loads of 1000 N, 1500 N and 750 N at 1 m, 2 m and 2.5 m from the left support. The Young's modulus for shaft material is 200 \(\rm \frac{GN}{m^2}\). Determine the frequency of transverse vibration.
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More Mechanical Vibrations Questions

Q1.At a certain speed, revolving shafts tend to vibrate violently in transverse direction. This speed is known as
Q2.Which of the following is TRUE for vibration of a mechanical system
Q3.A cantilever beam of cross section area 'A', moment of Inertia 'T' and length 'L' is having natural frequency ω1. If the beam is accidently broken into two halves, the natural frequency of the remaining cantilever beam ω2 will be such that
Q4.A mass of 2 kg is hung from the ceiling by a helical spring. When hung, the spring suffers an extension of 100 mm. If the mass is slightly displaced downward and released, it will oscillate at a frequency of (acceleration due gravity at the location is 10 m/s2)
Q5.The whirling speed of a rotating shaft depends on its _________.
Q6.For a single degree of freedom viscous damped system, if the frequency ratio is greater than √2, it implies that:
Q7.A suspended mass of 10 kg completes 40 oscillations in 20 seconds in a single-degree damped vibrating system. The stiffness of the spring is approximately _________. 
Q8.Consider a uniform shaft of length L fixed at its upper end and carrying a disc of the moment of inertia I at its lower end. The disc is twisted about the vertical axis and released. 'fa' is the natural frequency of the system when the shaft is assumed as massless, and 'fb' is the natural frequency of the system when the shaft is considered of the same moment of inertia as that of the disc. Find the ratio fa/fb.
Q9.A vibrating system having a mass of 30 kg is supported by 4 springs, each having a stiffness of k. The system runs at 420 rpm. If only 10% of the shaking force is allowed to be transmitted to the supporting structure, then the value of stiffness k will be close to:
Q10.A spring-mass system consists of a mass of 5 kg and two springs of stiffness 8 N/mm and 12 N/mm. The system is arranged in different manners, that is: (i) the mass is suspended at the bottom of two springs in series, and (ii) the mass is fixed between two springs. The ratio of natural frequencies of the case (ii) to those of case (i) is approximately ___________. 
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