Wereldsma 



n-,Q, 



^^3 I 



TURBINE 



I2 II 

 "2Q2 rLQ"i°i T, T2 



TT 



PROPELLERS 



Qt 



^2M5> 



Fig. 11 - Low-frequency analysis of contrarotating 

 propeller arrangement with epicyclic gearing 



Epicyclic Gearing— The basic construction of an epicyclic gearing and its 

 block diagram for the low-frequency behavior are shown in Fig. 11. The sum of 

 both propeller rpm's multiplied by their specific gear ratios equals the turbine 

 rpm under all conditions. The ratio between the rpm's of both propellers, how- 

 ever, is not predetermined, as in the case of a conventional gearing, but depends 

 on the characteristics and absorbed torques of both propellers. Therefore, the 

 propeller characteristics F^ and Fj are functions of nj and 03, as shown in the 

 diagram. The equations of motions of both propellers are 



(li + lG+A2l^) __J + AB It- ^ + Fj(ni, 02)01 = AQ^- - D^ , (2) 



(l2 + l2° + B2l^) -^ + AB I^.-^ + F2(o2,Oi) 02 = BQt - D2 . (3) 



In addition. 



+ B o» = o^ 



(4) 



248 



