Wereldsma 



DISCUSSION OF RESULTS 



Since the natural frequency of the measuring system amounts to approxi- 

 mately 600 Hz, the high frequency of blade encounter (approximately 400 Hz) 

 cannot be recorded without unacceptable dynamic error. 



The internal stiffness of the propeller influences the measurement sig- 

 nificantly when the natural frequencies of the individual propeller blades come 

 closer to the excitation frequency. Therefore the records of these high- 

 frequency phenomena must be seen as indicative rather than accurate. From 

 previous calculations (5) a dynamic amplification of the measuring system of 

 2.5 times can be estimated for this frequency. This figure must be taken into 

 account for the evaluations of the records of Fig. 7 and 8. It can be concluded 

 that the blade encounter excitation is small compared to the wake excitation. 

 Also the low- frequency interaction is small compared to the blade frequency 

 signals, as is illustrated in Figs. 5 through 8. 



The unequal wake is still the dominating input for both propellers, and the 

 interaction of both propellers is shown to be less significant. The relative am- 

 plitudes of excitation are comparable with those of single propellers. Since the 

 total propulsive power is divided between the two propellers, the absolute value 

 of the excitations is favorable. The sum of the absolute excitations of both pro- 

 pellers, in the axial direction as well as in the lateral direction, is shown to be a 

 compromise between the behavior of a single four-bladed and five-bladed pro- 

 peller having the same power absorption. 



For this combination of a four-bladed and a five-bladed propeller it appears 

 that the high-frequency interaction is negligible in the axial direction and de- 

 tectable in the lateral direction. It can be expected that for a combination of 

 propellers with an equal blade number this interaction is negligible in the lateral 

 direction and relatively large in the axial direction, due to the simultaneous 

 blade encounter of all the blades. 



FURTHER STEPS FOR THE DYNAMIC ANALYSIS 

 OF CONTRAROTATESfG PROPULSION SYSTEMS 



To obtain insight into the vibratory behavior of a contrarotating propulsion 

 system as installed aboard a ship, indications will be given about the dynamic 

 analysis of the shafting. The analysis will be split in two parts: (a) the low- 

 frequency behavior in the torsional direction, taking into account the modulation 

 of the propeller speed, due to the fluctuating propeller loading caused by ship 

 motions and orbital water motions, and (b) the high-frequency behavior in the 

 torsional and axial directions, describing the propeller vibrations resulting from 

 the fluctuating propeller loading due to the unequal ship's wake. For both types 

 of analysis it is assumed that a turbine engine is installed. 



Low- Frequency Behavior 



For the analysis of the low- frequency behavior the internal elasticities of 

 the shafting and gearing system are neglected. 



246 



