Question

Whirling speed of a shaft coincides with the natural frequency of its:

• A. Longitudinal Vibrations
• B. Transverse Vibrations
• C. Torsional Vibration
• D. Combined torsional and longitudinal vibrations

Hint:

Whirling or critical speed is a resonance phenomenon where the rotational frequency excites the natural bending frequency of the shaft. Think of a jump rope – when you spin it at a certain speed, it forms a large wave. This is analogous to whirling.

Answer 1

The Correct Option is B

Step 1: Understand the concept of whirling speed.
Whirling speed, also known as critical speed, is the angular speed at which a rotating shaft tends to vibrate violently in the transverse direction. This phenomenon occurs when the frequency of rotation coincides with one of the natural frequencies of transverse vibration of the shaft-mass system. Step 2: Understand the different types of shaft vibrations.
A rotating shaft can experience different types of vibrations:
Longitudinal Vibrations: These occur when the particles of the shaft move parallel to the axis of the shaft. The natural frequency of longitudinal vibration depends on the shaft's material properties (Young's modulus), length, and cross-sectional area.
Transverse Vibrations: These occur when the particles of the shaft move perpendicular to the axis of the shaft. The natural frequency of transverse vibration depends on the shaft's material properties (Young's modulus), length, cross-sectional area (through the moment of inertia), and the mass distribution along the shaft.
Torsional Vibrations: These occur when the shaft twists about its axis. The natural frequency of torsional vibration depends on the shaft's material properties (shear modulus), length, and polar moment of inertia. Combined Vibrations: These involve a combination of the above modes. Step 3: Relate whirling speed to natural frequencies.
Whirling speed is specifically associated with the bending or bowing of the shaft, which is a form of transverse vibration. When the rotational frequency of the shaft matches a natural frequency of its transverse vibration, resonance occurs, leading to large amplitude transverse deflections (whirling). Step 4: Eliminate incorrect options.
Option 1 (Longitudinal Vibrations): Whirling is a bending phenomenon, not an axial oscillation.
Option 3 (Torsional Vibration): Torsional vibration involves twisting, not bending. Whirling is a bending instability.
Option 4 (Combined torsional and longitudinal vibrations): While complex scenarios can involve coupled vibrations, the fundamental phenomenon of whirling speed is primarily linked to transverse vibrations.
Step 5: Identify the correct option.
The whirling speed of a shaft coincides with the natural frequency of its transverse vibrations.