The whirling speed of a rotating shaft is the same as the frequency of the shaft in.
Natural transverse vibration
Whirling Speed and Rotating Shafts
The whirling speed of a rotating shaft is a critical concept in the field of machine dynamics and design. It is also commonly referred to as the critical speed. This speed represents a specific rotational velocity at which the shaft experiences severe lateral (transverse) deflections, leading to instability. This phenomenon occurs due to the principle of resonance.
Shaft Vibration and Resonance
Every elastic body, including a rotating shaft, possesses inherent frequencies at which it naturally tends to vibrate when disturbed. These are known as natural frequencies. When the rotational speed of a shaft matches one of these natural frequencies, particularly a natural frequency associated with transverse (bending) vibration, the shaft enters a state of resonance. In this resonant condition, even minor imbalances or disturbances can cause vibrations with very large amplitudes, which can result in significant damage to the shaft itself and its supporting bearings.
- Whirling Speed (Critical Speed): This is defined as the specific rotational speed at which the operating frequency of the shaft coincides with its natural frequency of transverse vibration.
- Resonance: This is a physical condition where the frequency of an applied periodic force (in the case of a rotating shaft, the rotational speed creating an imbalance force) becomes equal to the natural frequency of the system. This equality leads to the maximum possible amplitude of vibration.
Natural Transverse Vibration Explained
The question focuses on identifying the specific type of vibration frequency that corresponds to the whirling speed of a rotating shaft. Let's clarify the key terms involved:
- Natural Vibration: This refers to the inherent tendency of a system to vibrate at its characteristic frequencies without the continuous application of an external periodic driving force. Once an initial disturbance is applied, the system vibrates at these natural frequencies, which are determined by its material properties, geometry, and how it is supported.
- Transverse Vibration: This is a mode of vibration where the particles of the vibrating body move perpendicular to the main axis of the body. For a rotating shaft, transverse vibration means the shaft bends or deflects sideways, away from its central axis of rotation. It is also often called lateral vibration.
When a rotating shaft reaches its whirling speed, its rotational frequency becomes exactly equal to its natural frequency of transverse vibration. This precise match triggers resonance, resulting in significant lateral deflections. Therefore, the term "Natural transverse vibration" accurately describes the frequency associated with whirling speed.
Comparing Vibration Types for Whirling Speed
To further understand why natural transverse vibration is the correct answer, let's compare it with the other options:
| Vibration Type | Description and Relevance to Whirling Speed |
|---|---|
| Natural Transverse Vibration | This is the direct cause of whirling. Whirling speed occurs precisely when the shaft's rotational speed matches its natural frequency of bending or lateral (transverse) vibration. This leads to resonance and large deflections perpendicular to the shaft's axis. |
| Forced Longitudinal Vibration |
Forced Vibration: This type of vibration occurs when an external, periodic force continuously drives the system to vibrate at the frequency of that external force. Longitudinal Vibration: This vibration involves particles moving parallel to the axis of the body. For a shaft, this means it would be stretching and compressing along its length, rather than bending sideways. Whirling speed is not primarily linked to forced longitudinal vibrations. While external forces can induce forced vibrations, whirling specifically denotes a resonance condition that involves the shaft's own mass and elasticity in bending (transverse motion). |
| Natural Longitudinal Vibration | This refers to the shaft's inherent tendency to vibrate by extending and contracting along its length. Although a shaft does have natural longitudinal frequencies, the phenomenon of whirling speed is related to lateral instability and bending, not axial movement. |
| Forced Transverse Vibration | This would imply that an external periodic force is causing the shaft to bend, and the frequency of this external force matches the transverse vibration. While a shaft can indeed undergo forced transverse vibrations, the term "whirling speed" specifically refers to a resonance condition where the rotational speed of the shaft itself acts as the exciting frequency, matching one of the shaft's *natural* frequencies, not an independent, external forced frequency. |
In conclusion, the whirling speed of a rotating shaft is the rotational speed at which the shaft resonates with its inherent (natural) tendency to vibrate by bending (transverse vibration). This critical resonance makes natural transverse vibration the correct answer.
Important Questions from Resonance and Whirling - Teaching
Whirling speed of a shaft coincides with the natural frequency of its
