The Vibratory Output of Contrarotating Propellers 



EQUATIONS OF MOTIONS OF CONTRA ROTATING PROPELLER ARRANGEMENT 

 I * I Qf L I Ofh I Of L I QfI X ^ I °''L +[°Z1* , I °f I '» J QfL ^ 1 ^ ^ L.i - q 



Mf Xf ♦ K Xp ♦ II Xp ♦ IlUf ♦ II *F + - 



I ^ Oa L Qa 



'a *a ♦ \—^\ *a + — ^ 



^ X. . ^ . *, = Tf 

 Z^F Z,*p 



J_ 

 z * 



z .1 



z * 



MECHANICAL ADDED MASS AND 

 MASS OF DAMPING OF THE 



PROPELLERS INDIVIDUAL 



PROPELLERS 



MUTUAL HYDRODYNAMICAL COUPLING MECHANICAL SUPPORT OF EXCITATION 



FORWARD AND PROPELLER 

 AFT COUPLING SHAFTS 



BY THE SHAFT (DRIVING POINT 

 (TRANSFER IMPEDANCE) 



IMPEDANCE) 



EXCITATIONS ARE CAUSED BY THE WAKE AND THE MUTUAL PROPELLER INTERFERENCE 

 Tp = THRUST EXCITATION OF FORWARD PROPELLER 

 Of = TORQUE EXCITATION OF FORWARD PROPELLER 

 Ta = THRUST EXCITATION OF AFT PROPELLER 

 Qa = TORQUE EXCITATION OF AFT PROPELLER 



Fig. 13 - Equations of motions for high-frequency analysis 

 of a contrarotating propeller arrangement 



coupling of both propeller shafts and introduced by the gearing and turbine, 

 are taken into account. 



For both propellers the normal added mass, damping, and individual cou- 

 pling coefficients can be distinguished. In addition 16 coefficients, representing 

 the mutual hydrodynamic propeller interactions, are introduced. Further inves- 

 tigations are required to estimate the importance or negligibility of the coeffi- 

 cients, before calculations of the forced vibrations resulting from the experi- 

 mentally determined excitations of the propellers can be started. 



CONCLUSIONS 



1. The unequal inflow of the ship's hull is still the dominating cause of the 

 unsteadiness in the operation of both propellers of a set of contrarotating pro- 

 pellers. The fluctuating thrust and torque, expressed as a percentage of their 

 mean values, amount to about the same value as for single- propeller arrange- 

 ments. The lateral effects show a reduced amplitude. The absolute excitations 

 reduced by the division of the total power over two propellers, may result in 

 advantages. 



2. The number of blades of both propellers is an essential parameter in the 

 vibratory interaction problem. For the case of a four-bladed and five-bladed 

 propeller the interaction can be divided into a low- frequency and a high- frequency 

 range (respectively below blade frequency and above 3 times the blade frequency). 



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