Question

A shaft carrying a rotor at the mid span has a critical speed 'N'. If the diameter of the shaft is increased by 25% and the distance between the bearings is reduced by 25% the critical speed will be

• A. $\sqrt{\frac{5}{4}}N$
• B. $\frac{25}{6\sqrt{3}}N$
• C. $\frac{6\sqrt{3}}{25}N$
• D. $\frac{25}{\sqrt{27}}N$

Answer 1

The correct option is B $\frac{25}{6\sqrt{3}}N$

$N_{cr}\alpha \sqrt{\frac{EI}{m{l}^3}}I=\frac{\pi d^4}{64}$

$\therefore N_{cr}\alpha \sqrt{\frac{d^4}{l^3}}$

$\frac{N_2}{N1}=\sqrt{\frac{d_2^4}{d_1^4}}\times \sqrt{\frac{1_1^3}{1_2^3}},$

$N_1=N$

$N_2=\sqrt{\frac{{1.25}^4}{{0.75}^3}}N$

$N_2=\frac{25}{6\sqrt{3}}N$