﻿124 Mr. 0. Rodger s on the Vibration 



is shown that in addition to producing the ordinary static 

 deflexion, the action o£ gravity is such as to cause a double 

 frequency ripple in the whirl which would tend to reach a 

 maximum at half the first critical speed. The magnitude of 

 this ripple is, however, proportional to the square of the 

 amount by which the rotor is out of balance, and would 

 therefore fail to appear in a well-balanced machine. In any 

 case the effect is very small. 



It is then shown that a rotor with bi-polar asymmetry, 

 such as exists in a rotor slotted for a two-pole winding, may 

 show a double frequency vibration at half the critical speed 

 even when the rotor is perfectly balanced, so that such a 

 machine might vibrate at half the critical speed even when 

 it would run perfectly at the full critical speed. Vibration 

 arising from this cause could not, therefore, be rectified by 

 balancing, and this is the only case met with where improved 

 balancing would not effect an improvement in the running. 

 This case is gone into in some detail, and it is shown that 

 the motion here also is a circular whirl of double frequency, 

 that is, of twice the speed of rotation of the machine. If, in 

 addition, the machine is out of balance, a triple frequency 

 effect might appear, but is not likely to do so. 



The effect is then discussed of lack of proportionality in 

 the deflexion of the shaft and again the possibility appears 

 of vibration appearing at half the critical speed, but only if 

 the machine is not properly balanced. The effect is then 

 gone into of fluctuations in the angular velocity through 

 variations in the driving torque, and of resonance between 

 the rotor and the foundations or other masses outside the 

 machine, from which it appears that marked vibration might 

 appear at almost any speed through either of these causes. 



The effect of friction on ihe transverse vibration is then 

 discussed, and the results are given for the case where the 

 frictional resistance varies as the first power of the speed, 

 and also where it varies as the second power of the speed, 

 the latter being more probably in accordance with the facts 

 than the former. It is shown that the maximum vibration 

 appears in both cases at a speed equal to the stationary 

 critical speed, also that the phase difference between the 

 force due to the out-of-balance and the displacement 

 depends on the amount of friction, and also on the speed. 

 If the frictional forces vary as the square of the speed, as 

 is probably the case, the angle varies also with the amount 

 by which the rotor is out-of-balance. 



Some effects of viscosity of oil in the bearings, and of 

 different bearing clearances are then gone into. 



