Consider the following statements regarding whirling of a shaft : 1. The bending of the shaft depends upon the eccentricity of the centre of mass of the rotor, as also upon the speed at which the shaft rotates. 2. Whirling speed is the speed at which the shaft does not vibrate at all. 3. When rotor is mounted on a shaft, its centre of mass does not usually coincide with centre line of the shaft. Which of the above statements are correct?
Whirling of Shaft: Statement Analysis
This question asks to identify the correct statements regarding the phenomenon of shaft whirling, also known as critical speed.
Statement Analysis
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Statement 1: The bending of the shaft depends upon the eccentricity of the centre of mass of the rotor, as also upon the speed at which the shaft rotates.
- Analysis: This statement is correct. Whirling occurs due to the imbalance caused by the center of mass (CM) not coinciding with the geometric center of the shaft. This eccentricity creates a dynamic force that increases with speed. The bending (deflection) amplifies significantly, especially near the critical or whirling speed.
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Statement 2: Whirling speed is the speed at which the shaft does not vibrate at all.
- Analysis: This statement is incorrect. The whirling speed, or critical speed, is the specific rotational speed at which the shaft experiences resonance. At this speed, even small imbalances cause large amplitude vibrations, potentially leading to failure. It is the speed of maximum vibration, not zero vibration.
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Statement 3: When a rotor is mounted on a shaft, its centre of mass does not usually coincide with the centre line of the shaft.
- Analysis: This statement is correct. Due to manufacturing imperfections, uneven mass distribution, or mounting inaccuracies, the rotor's center of mass rarely aligns perfectly with the shaft's axis of rotation (centerline). This misalignment is the fundamental cause of dynamic imbalance that leads to whirling.
Conclusion
Based on the analysis, statements 1 and 3 are correct, while statement 2 is incorrect.
Therefore, the correct option is the one that includes statements 1 and 3 only.
Important Questions from Resonance and Whirling
- Whirling of a shaft occurs when natural frequency of transverse vibration ________.
According to Dunkerley’s empirical equation, the frequency of the transverse vibration of the system of several loads attached to the same shaft is
If two nodes are noticed at a frequency of 1800 rpm during whirling of a simply supported long slender rotating shaft, determine the first critical speed of the shaft (in rpm).
The rotor shaft of a large electric motor supported between short bearings at both the ends shows a deflection of 1.8 mm in the middle of the rotor. Assuming the rotor to be perfectly balanced and supported at knife edges at both ends, the likely critical speed (in rpm) of the shaft is
An automotive engine weighing 240 kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of 16 MN/m while the stiffness of each rear spring is 32 MN/m. The engine speed (in rpm), at which resonance is likely to occur, is
