Question

Critical speed of a shaft depends upon its

• A. mass
• B. stiffness
• C. mass and stiffness
• D. stiffness and eccentricity

Hint:

Higher stiffness increases critical speed, while higher mass reduces it.

Answer 1

The Correct Option is C

Step 1: Understanding critical speed.
Critical speed of a shaft is the speed at which the shaft’s natural frequency of transverse vibration coincides with its rotational speed, leading to resonance and large deflections.
Step 2: Relation with natural frequency.
The critical speed \( \omega_c \) of a shaft is directly related to its natural frequency \( \omega_n \), which for a single degree of freedom system is given by: \[ \omega_n = \sqrt{\frac{k}{m}} \] where \( k \) is the stiffness of the shaft and \( m \) is the mass associated with the shaft.
Step 3: Identifying governing parameters.
From the expression, it is clear that the natural frequency—and hence the critical speed—depends on both the mass and the stiffness of the shaft.
Step 4: Conclusion.
Therefore, the critical speed of a shaft depends on its mass and stiffness.