Due to practical limitations the number of measuring points during operation was rather small. In order to get more accurate mode shape and damping estimates especially for higher modes it is recommended that more measuring points should be included in the analysis. However, in this case the used configuration was able to identify parameters for lowest modes of the thruster reasonably well, especially natural frequencies. Table 2 Experimental modal analysis results In dry dock During operation in water (OMA) frequency (fi/fref) damping (ȗi/ȗref) frequency (fi/fref) damping (ȗi/ȗref) description - - 0,218 0,97 Global mode of the ship hull (apparently vertical bending) 0,906 1,69 0,279 4,31 Rotation around steering axis - - 0,402 0,34 Global mode of the ship hull (apparently torsion) 0,826 0,34 0,707 0,71 1st transversal mode 1,000 1,00 0,911 1,63 1st longitudinal mode 2,217 1,51 1,944 1,49 Vertical bending of the rotor, vertical translation of the thruster in phase 2,501 0,83 - - Vertical bending of the rotor, vertical translation of the thruster out of phase 3,061 1,40 2,178 1,40 Transversal bending of the rotor, rotation of the thruster around steering axis out of phase Numerical Results and Correlation with Experiments Azimuthing Thruster in Air Before analyses the mass of the model of the mechanical structure was calculated. It was noted that the mass of the model was about 2 % smaller than weighted mass of the real structure. Considering the simplifications in the model the difference is quite small. The ship had two azimuthing thrusters symmetrically both side of the centre line of the ship hull. Symmetrical boundary condition was applied at the centre line of the ship structure model in most of the analyses. Symmetric boundary condition implies that the thrusters vibrate transversally out of phase. At the other edges of the ship model displacements were fixed. Natural modes were also calculated with anti-symmetric boundary condition at the centre line, which implies that the thrusters vibrate in phase. The calculated transversal mode of the thruster with anti-symmetric boundary condition was about 2% higher than with symmetric boundary condition. Differences for the other global modes were negligible. Thus, it was concluded that coupling between the thrusters modes was rather small. Influence of stiffness of the slewing bearing on the thruster modes was studied. Because the stiffness of the bearing depends on the loading, the stiffness was calculated with different loading scenarios. At first, gravity of the thruster was applied as evenly distributed load for the upper axial bearing. The lower axial bearing was assumed to have a clearance between rolling elements and bearing races, thus having no contact force and no stiffness. The goal was to simulate the corresponding modal testing condition in dry dock. It was found that frequency of the lowest transversal mode was about 6 % higher than the measured one and frequency of the longitudinal mode was about 3 % smaller than the measured one. Calibration measurements with static external force were also simulated in order to study static stiffness of the thruster. Results showed that the static stiffness in the transversal direction was about 9 % higher than measured one and stiffness in the longitudinal direction was about 4 % smaller than measured one. 12
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