Question

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 the ends, the likely critical speed (in rpm) of the shaft is

• A. 350
• B. 705
• C. 2810
• D. 4430

Answer 1

The correct option is B 705

Critical or whirling speed,

${\omega }_c={\omega }_n=\sqrt{\frac{K}{m}}=\sqrt{\frac{g}{\delta }}\text{Hz}$

If $N_c$ is the critical or whirling speed in rpm then

$\frac{2\pi N_c}{60}=\sqrt{\frac{g}{\delta }}$

$\Rightarrow \frac{2\pi N_c}{60}=\sqrt{\frac{9.81m/s^2}{1.8\times {10}^{-3}m}}$

$\Rightarrow N_c=705.32\text{rpm}$ $\approx 705\text{rpm}$