The Vibratory Output of Contrarotating Propellers 



Comparison of Both Systetns — We assume that the turbine rpm is constant, 

 which is reasonable from a, practical viewpoint, due to the large moment of in- 

 ertia of the turbine. For the conventional gearing it follows simply that also 

 both propeller rpm's are constant. No excessive differences between single or 

 contrarotating propeller turbine installations can be expected. For the epicyclic 

 gearing, however, it follows from Eq. (2) 



cin2 



B dt 



and, for small deviations from the nominal rpm, 



A ' 



(5) 



(6) 



Combining Eqs. (2) through (6) we obtain for epicyclic gearing the following rela- 

 tions between the disturbances Dj and B^ and the speed of the propellers: 



^? 



§ (I. + I2^) 



dn J 

 "dT 



Fj(nj,n2) + 



F^Cnj.rij) 



-D, . |d,('-) 



;(!f ('.-■'?' 



+ I.+ 1 



2'\ dt 





D.+f D,. 



(7b) 



From these equations follows, in contrast to conventional gearing, that rpm 

 fluctuations of both propellers will still occur, due to disturbances from sea- 

 waves, even if the turbine rpm is kept constant. Therefore, it is expected that, 

 in comparison with the conventional gearing, larger deviations from the nominal 

 rpm of both propellers will occur. From Eq. (7) follows additionally 



, „. dn, ^ „. dn, 



(Ii + Ip) -^ + Fj(ni,n2)nj + D^ = A {l, + l^) -^ + F2(n2, 0^)02 + D2 



This formula shows that the low-frequency torque variations of both propellers 

 are their mutual reactions. For the steady state conditions without disturbances 

 Dj and D2, 



B[Fj(nj,n2) Hj] = A [F2(n2, Oj) Hj 1 • 



This relation also follows from the equilibrium conditions of the planet wheels 

 of the gearing. 



Remarks 



1. In general it can be concluded that, in comparison with the conventional 

 gearing, for the epicyclic gearing stronger frequency modulations of the fluctuat- 

 ing forces can be expected and as a consequence stronger requirements have to 

 be fulfilled to avoid critical shaft vibrations. 



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