A vibration test is run to check the design adequacy of bearings A and B. The unbalanced

Question:

A vibration test is run to check the design adequacy of bearings A and B. The unbalanced rotor and attached shaft have a combined mass of 2.8 kg. To locate the mass center, a torque of 0.660 N ∙ m is applied to the shaft to hold it in equilibrium in a position rotated 90° from that shown. A constant torque M = 1.5 N∙ m is then applied to the shaft, which reaches a speed of 1200 rev/min in 18 revolutions starting from rest. (During each revolution the angular acceleration varies, but its average value is the same as for constant acceleration.) Determine

(a) The radius of gyration k of the rotor and shaft about the rotation axis,

(b) The force F which each bearing exerts on the shaft immediately after M is applied,

(c) The force R exerted by each bearing when the speed of 1200 rev/min is reached and M is removed. Neglect any frictional resistance and the bearing forces due to static equilibrium.