Analytical procedures for torsional vibration analysis of ship power transmission system

Abstract In this paper two relatively simple analytical procedures for free and forced torsional vibration analysis of ship power transmission systems are developed. In the first, approximate procedure, the shaft line is modelled as a two-mass system and analytical solution of the differential equations of motion is given. In the second one, a multi degree of freedom (d.o.f.) problem of the complete propulsion system is solved by the Rayleigh-Ritz method. A special attention is paid to the determination of the contribution of each cylinder to the primary and secondary engine torques by taking into account the firing order. The application of the two procedures is illustrated in the case of a typical propulsion system of a merchant ship with a slow-speed main engine connected directly to the propeller by a relatively short shaft line. The obtained results are verified by a comparison with measurements. All classification societies require calculation of the propulsion system operating parameters, but they do not provide simplified formulae for vibration analysis. The outlined analytical procedures can be used for the estimation of torsional vibration of the shaft line in the preliminary ship design stage as well as for ships in service.