14. starptautiskÄ konference 2012 - Latvijas JÅ«ras akadÄmija

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̇̇Proceedings of 14th International conference „Maritime Transport and Infrastructure - <strong>2012</strong>”Fig. 1. Main engine and shaft simplified modelThe simplified shaft system consists of the main engine, shaft and propeller.̇ ̇(3)where= reduction gear inertia =propeller gear inertia= damping coefficient = stiffness factor=stiffness factor= reduction gear torque= reduction gear angular displacement = distance from propeller to reduction gear=reduction gear angular displacementIn the Lagrange equation method to derive to dynamic equations of this system:where in prospect of̈ ( ̇ ̇ )[ ] [ ̈̈̈ ( ̇ ̇ ) ( )] [ ] [ ̇̇] [ ] [ ] [ ](4)Natural frequencies can be determined in case of vibration without forces.LetThus, from[ ] [ ] [ ] (5)Hereis a solution. However, this solution means, motion of the system equal tozero that acceptance. Here is the solution make the desired solution is not equal to zero uniformly;128
Proceedings of 14th International conference „Maritime Transport and Infrastructure - <strong>2012</strong>”according to the linear algebra determination of the design matrix on the left column must be equal tozero.det| |=0( ( )settingThe complete solution can be written as;( )Thus, the natural frequencies were determined as 10.189 rad/s for reduction gear and 1.112rad/s for propeller.and2. Torsional Vibration Response of Calculation and AnalysisIn this study, fishing boat has been taken a base which particulates are length 20 m, width 5.7m, depth 2285m and MAN 8L 32/40 is considered as a main engine. The considered ship andpropulsion system is shown in Figure 2.Torsional vibrations occupy because inertia forces (due to resistance elements formed in therotary shafts) try to block angular displacement of two points at rotating shafts. Torsional vibration isnot distinctive as bending vibration at bearings and should be control in depth. Without any signs,torsional vibrations give rise to very dangerous consequences (Maurice [8]).Fig. 2. Base on ships and main engine, propulsion systems (MAN [9])The main engine that considered consists of 8 cylinder diesel engine. It is assumed that theengine is operated at the constant speed of 750 rpm. The specific parameters about this engine are allgiven in table 1 for calculating the torsional vibration.129
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14. starptautiskÄ konference 2012 - Latvijas JÅ«ras akadÄmija

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