Conclusions Close results were obtained from finite element analyses and experimental investigations. Maximum difference between calculated and experimentally determined natural frequencies in air was about 4 %. The calculated global natural frequencies in water also corresponded reasonably well with the measured ones. Due to the surrounding water natural frequencies of the lowest longitudinal and transversal modes were degreased in this case about 5 % and 14 %, respectively. Based on the modeling method presented in this paper, sufficiently accurate calculation results can be achieved. From the modeling point of view the following conclusions can be made: • Slewing bearing stiffness and local stiffness of ship affect significantly natural frequencies and modes • Shaft line bending modes are strongly coupled with the global modes of the thruster body • Fluid-structure interaction can be modeled with sufficient accuracy with the used modeling method • Stiffness of the hydraulic steering system dominates the thruster rotation modes around steering axis • Electromechanical interaction has only minor effect on the natural frequencies for this type of azimuthing thrusters The presented case study proved applicability of OMA and ODS analyses in challenging operating conditions where conventional modal testing is practically impossible. These analyses provided necessary information for model verification. 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 used configuration was able to identify parameters for lowest modes of the thruster reasonably well. In the future studies it is recommended that the gyroscopic effect will be taken into account with the whole model of the azimuthing thruster. This can be done for example by combining rotor model and the thruster body model using substructuring technique. Acknowledgements This paper is based on Master’s Thesis “Modelling of Vibratory Behaviour of Azimuthing Thruster”, in finnish. The thesis has been done for Helsinki University of Technology for department of Applied Mechanics in 2009. Financial support for this study was provided by ABB Marine. References 1. Pilkey, Walter D. Formulas for stress, strain and structural matrices. John Wiley & Sons Inc, New York, ISBN 0-47152746-7 1458 p. 1994. 2. Harris, Tedric A. Rolling Bearing Analysis. 4th Edition. John Wiley & Sons Inc, ISBN 0-471-35457-0, 1086 p. 2001. 3. Merritt, Herbert E. Hydraulic Control Systems. John Wiley & Sons, ISBN 0471596175. 357 p. 1967. 4. Jelali, Mohieddine & Kroll, Andreas. Hydraulic Servo-systems: Modelling, Identification, and Control. Springer, ISBN 1852336927, 9781852336929. 355 p. 2003. 5. Merrill, E.F. Dynamics of AC electrical machines. Industry Applications, IEEE Transactions on, Vol. 30:2. pp. 277285. 1994. 6. Ehrich, Fredric F. Handbook of Rotordynamics. McGraw-Hill, ISBN 0070193304. 496 p. 1992. 17
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