﻿On the Vibration and Critical Speeds of Rotors. 123 



A single part rotor can vibrate in either of two ways, as 

 shown in figures 1 and 2, or in a manner which is a combi- 

 nation of the two motions : — 



Fig. 1. Fig-. 2. 







Fig. 1 shows a purely transverse vibration, while in fig. 2 

 the motion is solely one of oscillation about the centre of 

 gravity. In the transverse vibration the conditions are 

 clearly the same whether the rotor body is a disk or is 

 cylindrical ; but in the case of the oscillation, the motion, 

 owing to the gyrostatic effects called into play, depends 

 both on the proportions of the rotor and the speed at which 

 it is running. 



The speed at which transverse vibration becomes a maxi- 

 mum we shall call the "first critical speed/' and that at 

 which the oscillation becomes a maximum, the "second 

 critical speed," as the latter is in all practical cases con- 

 siderably higher than the former. 



The following is a general outline of the treatment adopted 

 and the conclusions reached : — 



Section 1 deals with the vibration of a rotor when not 

 running, and a relationship is deduced between the fre- 

 quencies for the transverse motion and for the oscillation 

 which we shall call respectively the " stationary first critical 

 speed," and the " stationary second critical speeds." 



The second section deals with the transverse vibration, 

 frictional resistance being ignored. It is first showm that 

 there appears to be no foundation for the frequently ex- 

 pressed view that there is a possible region of marked 



vibration at — ^ times the first critical speed, as such a 



conclusion can only be reached through an incorrect assump- 

 tion with regard to the conditions. It is then shown that 

 the motion or vibration is a circular whirl about the statically 

 deflected position of the shaft, and that this motion reaches 

 a maximum at a speed equal to the stationary first critical 

 speed. The magnitude of the whirl is proportional to the 

 amount by w'hich the machine is out of balance, so that 

 the main vibration here dealt with should disappear with 

 good balancing. 



The action of gravity is then gone into more fully, and it 



