Question

The critical speed of a rotating shaft depends on

• A. Mass and stiffness
• B. Mass and eccentricity
• C. Stiffness and eccentricity
• D. Mass, stiffness and eccentricity

Hint:

While the theoretical natural frequency of the shaft depends strictly on mass and stiffness, the actual physical critical speed behavior, including dynamic deflection and stability limits, is heavily influenced by the eccentricity of the rotating mass.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
This question deals with the physical parameters that influence the critical speed (or whirling speed) of a rotating shaft carrying a rotor.

Step 2: Key Formula or Approach:
The critical speed of a shaft corresponds to its natural frequency of lateral vibration.
For a shaft carrying a rotor of mass $m$ with eccentricity $e$ and shaft stiffness $k$, the dynamic deflection $y$ at speed $\omega$ is given by:
\[ y = \frac{e}{\left(\frac{\omega_n}{\omega}\right)^2 - 1} \]
where $\omega_n = \sqrt{\frac{k}{m}}$ is the natural frequency of transverse vibration.

Step 3: Detailed Explanation:

• The natural frequency ($\omega_n$) depends on the mass ($m$) of the system and the stiffness ($k$) of the shaft.

• Eccentricity ($e$) is the distance between the center of gravity of the rotor and the geometric axis of the shaft.

• As the rotational speed approaches the critical speed, the eccentricity plays a vital role in determining the magnitude of the centrifugal force and the amplitude of vibration.

• In practical engineering systems, all three parameters (mass, stiffness, and eccentricity) dictate the vibrational amplitude and instability onset of the rotating shaft system.

Step 4: Final Answer:
The critical speed of a rotating shaft depends on mass, stiffness, and eccentricity.