Analytical procedures for torsional vibration analysis of ship power transmission system

• Published in: Engineering structures 2019-01, Vol.178, p.227-244
• Main Authors: Senjanović, Ivo, Hadžić, Neven, Murawski, Lech, Vladimir, Nikola, Alujević, Neven, Cho, Dae-Seung
• Format: Article
• Language: English
• Subjects: Analytical procedure; Cylinders; Differential equations; Electricity distribution; Engine excitation; Equations of motion; Firing (igniting); Naval engineering; Power transmission system; Propulsion system; Propulsion systems; Rayleigh-Ritz method; Shaft line; Ships; Torsion; Torsional vibration; Vibration; Vibration analysis
• ISSN: 0141-0296; 1873-7323
• DOI: 10.1016/j.engstruct.2018.10.035

•Condensed two-mass model of shaft line. Analytical solution of diff. eqs. of motion.•Simplified multi-mass model of shaft line. Rayleigh-Ritz method. Analytical solution.•Formulation of cylinder torque and engine primary and secondary torque.•Physically based transfer factor of engine excitation to shaft response.•Comparison with FEM. Verification by measurement. High accuracy. 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.