Sensitivity analysis showed that stiffness of the axial slewing bearing had significant effect on the natural frequencies, while stiffness of the radial slewing bearing had only minor effect. It was noted that displacements between the upper rolling elements and the bearing race due to gravity of the thruster were very small, significantly smaller than for instance flatness tolerance of the raceway. Also due to challenging construction and installation of the assembly block and the slewing bearing, it is very difficult to determine the real stiffness distribution of the slewing bearing. However, it is possible to study possible variation range of the stiffness. Assuming that gravity of the thruster is evenly distributed for rolling elements of the upper axial bearing and lower axial rolling elements to be just in contact with very low contact force, the stiffness of the whole slewing bearing was found to increase about 52 % compared to the previous case. Assuming that rolling elements of upper axial bearing are just in contact with very low contact force and lower axial bearing having a clearance between rolling elements and raceway, the stiffness was found to degrease about 45 %. By changing the stiffness of individual rolling elements of axial slewing bearing in the model within limits described above, close results with experiments were achieved, see Table 3. Difference between calculated and simulated static stiffness of the thruster was also smaller, about 4.7 % in the transversal direction and 0.5 % in the longitudinal direction. MAC-criterion was used to evaluate the correlation between experimentally determined and calculated mode shapes, see Fig. 10. As can be seen, diagonal values are over 70 % indicating good correlation for all modes except mode no 6 (transversal bending of the rotor). The rotation angle of the propeller was slightly different during testing compared to the model, which can be one possible reason for the low MAC value. Experimentally determined mode shapes were complex whereas numerically obtained were real modes. This can also contribute the MAC values. Table 3 Numerical and experimental natural frequencies in air Numerical Experimen tal Difference No Description Frequency (fi/fref) Frequency (fi/fref) (%) 1 1st transversal mode 0,840 0,826 1,7 2 Rotation around steering axis 0,929 0,906 2,6 3 1st longitudinal mode 0,990 1,000 -1,0 4 Vertical bending of the rotor, vertical translation of the thruster in phase 2,158 2,217 -2,7 5 Vertical bending of the rotor, vertical translation of the thruster out of phase 2,571 2,501 2,8 6 Transversal bending of the rotor, rotation of the thruster around steering axis out of phase 2,935 3,061 -4,1 Fig. 10 MAC values between experimental and numerical mode shapes in air Both experimental and numerical results showed that rotor modes are strongly coupled with the thruster. Therefore there is significant difference between frequencies of rotor transversal and vertical bending modes. In addition, the first vertical 13
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