bending mode was split into two modes, in the other mode the thruster body translates in phase and in the other mode the thruster body translates out of phase. Significant errors will be encountered if natural modes of the shaft line will be calculated without taking into account the whole azimuthing thruster and ship structure. Effect of the thruster body and surrounding structure on rotor bending modes are presented in Table 4. Table 4 Effect of the thruster body and surrounding structure on rotor bending modes Rotor model only, supported by bearings (spring elements) Whole model of the azimuthing thruster (rotor + thruster body + part of the ship structure) Measured, in air freq. (fi/fref) description freq. (fi/fref) description freq. (fi/fref) 2,158 1st vertical bending, vertical translational mode of the thruster body in phase 2,217 2,296 1st vertical bending 2,571 1st vertical bending, vertical translational mode of the thruster body out of phase 2,501 2,305 1st transversal bending 2,935 1st transversal bending, rotation of the thruster around steering axis out of phase 3,061 4,695 2nd vertical bending 4,856 2nd vertical bending 4,776 2nd transversal bending 5,224 2nd transversal bending Results of separate rotordynamic studies are presented in Fig. 11. The Campbell diagram presents lowest natural frequencies of the rotor as a function of the rotation speed. Excitation frequencies of rotation speed as well as blade frequency are also shown in the diagram. Intersection of these lines and curves of natural frequencies indicates critical speeds. As can be seen, the natural modes were split into forward and backward whirling modes. Difference between forward and backward whirling frequencies of first mode at typical rotation speed was about 7 %. These results were not verified by experiments, but influence of the gyroscopic forces on natural frequencies can be evaluated by presented studies. Fig. 11 Campbell diagram. Reference rotation speed nref is maximum rotation speed Natural frequencies of the shaft line were calculated with and without UMP. Due to UMP the natural frequencies of shaft line was degreased only about 0.4 %. The banding stiffness of the rotor in this case was very high compared to the forces of UMP. Therefore, electromechanical interaction has only minor effect on the natural frequencies for this type of azimuthing thrusters. 14
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