﻿156 Mr. P. Cormack on Harmonic Analysis of 



We then have : 

 The first critical speed c x is -^L =2020 R.P.M. 



The ratio of the radii of gyration k 1 jk 2 is 6/19 = 0*316. 



Half the distance between bearing centres = 53*5 ins. 



The radius of gyration for the cross moment of inertia 

 k 2 = 18-87 ins. 



The stationary second critical is, therefore, 



6' 2 = Cl x ^=- = 5730 R.P.M. 



From the curves, fig. 6, it will be seen that the main 

 oscillation will occur at 



5720x1-21 = 6940 R.P.M. 



and that a double frequency vibration may possibly show 

 itself at 



5730 x 0-515 = 3120 R.P.M. 



Thus a turbo-generator designed for a speed of 3000 R.P.M. 

 and having the above mechanical constants might show 

 marked vibration on the overspeed test. 





X. Harmonic Analysis of Motion transmitted by Hookers 

 Joint. By P. Cormack, A.B.C.Sc.L, Engineering Dept., 

 Royal College of Science for Ireland *. 



1. ^1|TITH the growth of high-speed machinery, the 

 H determination of the accelerations of machine 

 pieces becomes of increasing importance. These deter- 

 minations are considerably simplified by expressing in the 

 form of a Fourier Series the displacement of the piece 

 under investigation. The value of this method in the 

 analysis of the various phases of the motion of the mechanism 

 of the direct-acting engine is well known. It is here 

 proposed to investigate the coefficients of a Fourier Series 

 for the angular displacement of the driven shaft of a Hookers 

 Joint. The method being applicable to certain inversions of 

 the slider crank chain, these are also included. The ease 

 with which the coefficients can be determined, and calculations 

 made from the resulting series, make the study of these 

 mechanisms from this aspect one of considerable interest. 



* Communicated by the Author. 



