Answer to Question #172864 in Mechanical Engineering for George

Question

3.10 A rotating thin steel cylinder is replaced by a rotating thin aluminium cylinder

of the same mass, length and wall thickness. The stress due to rotation in

the aluminium cylinder is to be 25 % of that in the steel cylinder. Calculate the

allowable speed of the aluminium cylinder if the steel cylinder rotates at 600

r/min (relative density of steel = 7,8; relative density of aluminium = 2,9)

Answer 1

The force that provides the stress depends on the tangential speed of rotation at the walls of the cylinder:

$$f=k\rho\frac{v^2}{R}=k\rho\omega^2R,\\\space\\ f_a=0.25f_s,\\\space\\ \rho_a\omega_a^2R=0.25\rho_s\omega_s^2R,\\\space\\ \omega_a=0.25\omega_s\sqrt{\frac{\rho_s}{\rho_a}}=246\text{ rpm}.$$