﻿7?r 



and Critical Speeds of Rotors. 125 



In Section 3, the oscillatory vibration is dealt with, 

 taking into account the gyrostatic effects when the machine 

 is rotating, but ignoring the friction in order to keep the 

 expressions as simple as possible. It is there shown that 

 the gyrostatic effect causes the point of marked vibration to 

 occur at a higher speed than would be the case if the machine 

 were not rotating, and simple rules are given for calculating 

 this vibrating speed. An example is added to illustrate the 

 method of working the rules given. 



Much of the work on the main transverse vibration and 

 the main oscillatory vibration has been dealt with in various 

 forms by Ghree, Stodola, Morley and others, and the solution 

 for the transverse vibration with friction depending on the 

 first power of the speed has been given by H. H. Jeffcott 

 (Phil. Mag. March 1919), but the ground covered by the 

 remainder of the paper, particularly the question of sub- 

 sidiary critical speeds, does not appear to have received 

 much attention ; there is, however, in 'Engineering' a dis- 

 cussion where subsidiary critical speeds are touched on, 

 arising out of a paper by W. Kerr in that journal 

 (Feb. 18th, 1916). 



Section I. — Stationary Vibrations. 

 A. Transverse Vibrations. 



1. If M is the mass of the rotor body (the mass of the 

 shaft being being neglected), and we assume the rotor to be 

 perfectly balanced, the shaft will, when not rotating, show a 

 deflexion measured at the centre of gravity of the rotor of 



where a is the force required to produce unit deflexion. The 

 method of working out the static deflexion of the rotor for 

 actual cases is well understood and the value of a can be got 

 from the deflexion diagram. 



2. If now the rotor is set in vibration in a vertical plane, 

 the motion is represented by the following equation (using 



d 2 y 

 fluxional notation, where y is written for -~^ and y for 

 7 at 



^,etc.) 



■ ' My + <ry + M ff = (2) 



