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The critical speed of a uniform shaft with a rotor at the centre of the span can be reduced by
  • a)
    reducing the shaft length
  • b)
    reducing the rotor mass
  • c)
    increasing the rotor mass
  • d)
    increasing the shaft diameter
Correct answer is option 'C'. Can you explain this answer?
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Critical Speed of a Uniform Shaft with a Rotor

Introduction:
The critical speed of a shaft is the rotational speed at which the natural frequency of the shaft matches the frequency of the external load, causing excessive vibration and potential failure. The critical speed can be reduced by various means.

Options to reduce the critical speed:
a) Reducing the shaft length
b) Reducing the rotor mass
c) Increasing the rotor mass
d) Increasing the shaft diameter

Explanation:
Reducing the shaft length has no effect on the critical speed because the natural frequency of the shaft is inversely proportional to the shaft length. Therefore, reducing the shaft length increases the natural frequency and the critical speed.

Reducing the rotor mass reduces the external load on the shaft, which decreases the natural frequency and the critical speed. However, reducing the rotor mass may not be practical because it may affect the performance of the system.

Increasing the shaft diameter increases the stiffness of the shaft, which increases the natural frequency and the critical speed. However, increasing the shaft diameter may not be practical because it increases the weight and cost of the shaft.

Increasing the rotor mass increases the external load on the shaft, which decreases the natural frequency and the critical speed. However, increasing the rotor mass may not be practical because it may affect the performance of the system.

Conclusion:
Therefore, the best option to reduce the critical speed of a uniform shaft with a rotor at the centre of the span is to increase the rotor mass.
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