Shafts in the Neighbourhood of a Whirling Speed. 309 



so that while mco 2 is less than c, we have the condition 

 illustrated in fig. 2. 



When mar = c we have a; indefinitely great, and the value 

 of 'co is a critical speed. 



When ma) 2 is greater than c. we have the condition 



illustrated in fig. 3. Then 

 ma) 2 (x — a) =cx 



id x = 



The transition from one condition to the other in passing 

 through the critical speed is clearly brought out above when 

 the damping is included. 



5. The phenomena observed at balancing, as to the relation 

 of the (marked) point of maximum deflexion on the shaft's 

 periphery to the position of the mass centre, at speeds below, 

 in the neighbourhood of, or above the whirling speed are 

 well known to concord with the above phenomena due to 

 damping, and a reversal of the direction of rotation gives 

 results confirmatory of this. 



Thus in machines designed for testing the dynamic balance 

 of rotors, the part to be balanced is revolved in bearings 

 which are free to move to and fro between controlling spring 

 or rubber buffers which limit the amount of their motion in 

 a horizontal plane when the shaft vibrates. 



A scriber or pencil is held near the shaft at the section 

 being examined, and thus it is marked at that part of its 

 circumference that is most deflected. 



It is observed that at all speeds below the critical speed 

 an unbalanced body will be marked on the heavy side ; and 

 conversely above the critical speed it will be marked on the 

 light side. 



The mark, however, is not at the exact heavy or light 

 spot, but it is displaced angularly round the shaft, more or 

 less according to the proximity to the critical speed. The 

 direction of this angular displacement depends on the 

 direction of revolution of the body, and if displaced in one 

 direction by revolving clockwise, it will be equally displaced 



