14. starptautiskÄ konference 2012 - Latvijas JÅ«ras akadÄmija

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Proceedings of 14th International conference „Maritime Transport and Infrastructure - <strong>2012</strong>”DETERMINATION OF APPROPRIATE TORSIONAL VIBRATIONDAMPERS FOR A SHIP PROPULSION PLANTFatih Cüneyd Korkmaz*, Fuat Alarçin*Yıldız Technical University, Barbaros Bulvarı Besiktas ,Istanbul, E-mail: fkorkmaz@yildiz.edu.tr**Yıldız Technical University, Barbaros Bulvarı Besiktas ,Istanbul, E-mail: alarcin@yildiz.edu.trAbstractUnstable working performance of main engine and some other external disturbances are the mainreasons for vibration of propulsion plant of a ship. The most efficient encountered vibration istorsional vibration by reason of unsteady power loads and inertia forces on the ship main engine-shaftsystem. Crankshaft balancing weight as a passive system and torsional damping element as an activesystem are used in order to prevent this type of vibration. In this study angular motion of the mainengine-shaft and propeller plant was modeled using Lagrange Method and damping elements wereadded to the composed model to decrease the torsional vibration effect. Different damping valueswere tried to find appropriate torsional amplitude and velocity for the model. As shown in simulationresults, torsional vibration values of propeller-shaft system being up to ABS standards were obtained.KEY WORDS: Ship main engine propulsion systems, vibration analysis, Lagrange equationIntroductionVibratory forces generated in ship propulsion systems by some internal sources such as; mainengine, shaft, propeller, gearbox and by some external sources such as wave, current and imbalancedship loads are often unavoidable. These forces have influence on axial, radial and torsional vibrations.However their effect on propulsion system can be minimized or reduced by different isolationmethods. One of these methods the use of springs and damping elements for isolation between mainengine and its foundations.Rao [1] modeled the power transmission system with spring and damping element as fourdegreesof freedom system. Damping elements of the system were positioned between main engineand gearbox to reduce torsional vibration, and between thrust bearing and propeller to reduce lateralvibration. The springs were placed in between main engine, gearbox, bearings, propeller andfoundations. Radial forces and propeller thrust forces were thought of as moving forces on mainengine and propeller respectively. The equations of model were solved theoretically and thencalculated values of torsional vibration were compared to practically measured values. Some of thecalculated and measured values of frequencies are very close, while there are differences betweenthem for some cases, which is recognized as suitable for ISO vibration standards.Shu et al.[2] expressed torsional and axial vibrations of the engine crankshaft with Rayleighdifferential method. The engine crankshaft was modeled as a mass spring system to obtain easilynatural frequency of torsional and axial vibrations. Calculated results were compared with measuredresults and it is recognized that torsional vibration has an enormous effect on axial vibration thatcauses noise and vibration in engine.Grzadziela [3] carried out a study by using Matlab-Simulink, in which a propeller shaft systemhas four-degrees of freedom. In this study, the rotation torque of the main engine, fixed blade propellertorque, axial force and the shaft line bearings hydrodynamics effects have been taken intoconsideration. Model was established by using the Finite Element Method, the propeller shaft speedranges in different frequency values were determined according to different forms of support.Simulation results showed a maximum 10% error with the measured values converges.Hara et al.[4] established a main engine propeller shaft system with building block approachand analyzed the torsional, axial and lateral vibrations. The three dimensional solid model of the126
Proceedings of 14th International conference „Maritime Transport and Infrastructure - <strong>2012</strong>”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
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