Shaft torsion questions.

Question

Within the tertiary cooling system of a pressurised water cooler, a test circuit is set whereby an off-shoot rotor (magnets on a shaft) is required to transmit 3MW of power at 200rpm to a test-monitoring rig.

Assuming that we need a hollow shaft (to reduce mass during energy transmission) to transmit this power, what should be the dimension of the external diameter of this shaft if the internal diameter is specified at 0.75 of the external? The inspectorate have specified that the external diameter should not exceed 270mm; therefore, does this shaft conform to this specification? Explain.

{assume that the Nuclear Inspectorate have specified a condition that the maximum shear-stress due to load torsion along the shaft is not to exceed 55MN/m2}.

Answer 1

Hi James, 

 

First determine the maximum torque (T_max) that the shaft will be subjected to.  The maximum torque is power (3MW) divided by angular frequency (200rpm converted to rad/s).

 

Next calculate the polar moment of inertia in terms of the external radius, call it R. 

J = (pi/2)*[R^4 - (0.75R)^4]

 

Torsional shear stress (tau) is related to torque (T), distance from center (r), and polar moment of inertia (J) through:

tau = Tr/J

 

Torsional shear stress is largest at maximum torque (T = T_max) and on the surface of the shaft (r = R).  You can solve for the external radius by equating the maximum allowable torsional shear (55MPa) to the maximum torsional shear (T_max*R/J).

 

I hope this helps.  If you have specific questions on torsion problems, please feel free to contact me.  I am available for online tutoring.

 

Emma