﻿and Critical Speeds of Rotors. 129 



The whirling of the rotor is represented by the motion 

 of C about the undisturbed position of the shaft centre line, 

 i. e. by the rate of change of a. 



The " vibr.ition" of the rotor is judged in a general way 

 by the vibration of the bearings as felt when the hand is 

 applied to them. The force on the bearings is that applied 

 along OG by the deflexion r of the shaft, and vibration of 



the bearings arises through the varying position and magni- 

 tude of OC ; these in turn are due to the motion of the 

 ceritre of gravity G. 



2. If the machine is steadily rotating it might at first 

 sioht be thought that OC and CGr would be in the same 

 straight line, so that Gr would be steadily revolving together 

 with G about the undisturbed position of the shaft centre 

 line with an angular velocity n say. At the same time the 

 deflexion 00 = ?' might be changing its value and (neglecting 

 the weight of the rotor) the motion would thus be given by 



Mr — M?i 2 (V-f e) + ar = 0, 



or putting crjM = Ci 2 , 



r + (c x 2 — n 2 ) r = n 2 e, 



the solution of which is 



where Nx and y l are constants. 



We should thus conclude that r would become unlimited 

 Phil. Mag. S. 6. Vol. 44. No. 259. July 1922. K 



