14. starptautiskā konference 2012 - Latvijas Jūras akadēmija

Proceedings of 14th International conference „Maritime Transport and Infrastructure - 2012”crankshaft was analyzed by using the FEM and the equivalent beam model was constructed. Propellerwas modeled as a rotor, the properties like weight, inertia and polar moment of inertia were entered tothe equations and the additional mass of water was also taken into account. Bearings and rigidity ofthe body were considered as a spring in the model established. Vibration dampers placed in differentpositions were analyzed. Then results of the model were compared with measured results. Becausemain engine shaft system has many elements having damping effect, it can be concluded thatpredictions of these approaches for the model need to be accurate.Zhang et al.[5] investigated the influence of angular and axial forces acting on propeller bymodeling propeller and crankshaft. Frequency changes in torsional vibrations have been observedbetween the propeller and 1st order crankshaft journal, and between 5 th and 6 th order piston crankjournals. For axial vibrations, on the other hand, changes in frequency values are expressed almost thesame. Considering of coupled vibrations a nonlinear behavior effect was observed. They determinedthat large amount of errors would be experienced, when the propeller crankshaft analysis was assumedto be linear.MacPherson et al. [6] investigated methods to calculate the additional water mass of apropeller for vibration analysis. In this paper the effect of added mass on the torsional and axialvibrations of the propeller was examined. In order to calculate the added water mass of Weldsma BS-VII series of propellers a new formula and a new prediction was performed. The authors indicated thatthis prediction method would be beneficial for vibration analyses of propulsion systems because thereliability of the method have increased by the contribution of damping effect.In this study main engine, shaft and propeller system was modeled by Lagrange Method andthe model was solved by using Matlab-Simulink. Analysis of torsional vibration was put emphasisbecause it causes hazardous vibration. The aim of this paper is to apply an appropriate torsionaldamper with using different coefficient.1. Torsional Vibrations Modeling of Main Engine and Propulsion PlantKinetic, potential and damping energy were considered and described in form of LagrangeEquations [7];̇ ̇(1)where: Total Kinetic Energy,: Total Potential Energy,: Total Damping Energy,: Generalized forces (i=1,2,3,…,n),: Generalized coordinates (i=1,2,3,…,n),General formulation is represented the dynamic behavior of the mechanical systems in matrixform is expressed as follows.[ ]{ ̈} [ ]{ ̇} [ ]{ } { } (2)where[M], [D] and [K] indicate mass, damping effect and spring matrix respectively. express asa vibration disturbance effect and {x} represent displacement. As stated Fig. 1 is single degree offreedom. Motions of shaft propeller model are implemented by Lagrange method.Ships are enforced by many different dynamic and hydrodynamic forces. These forces areoccurred due to inside of the ships and also external loads. Large diesel reciprocating main enginesleads to an important force at low frequency. Ship propeller blade rate cause pressure fluctuations andthese changes cause vibration at the form of ship. If these internal and external shocks and harmonicsfrequencies of the force encounter natural frequencies of the structure, a resonant condition will occur.127