The propulsion shaft system, as the core of the ship’s power system, has attracted widespread attention in terms of vibration. This paper is dedicated to the study of the dynamic response characteristics of the ship propulsion shafting system, with a particular focus on the impact of the shaft-driven generator supported by bearings on the dynamic torque of the shafting system. A classic lumped-parameter equivalent system model is adopted, and the time domain transient response simulation calculation is conducted based on the Newmark-β method. A comprehensive analysis is made of the vibration torque and vibration stress in the propulsion shaft system under different rotational speeds and working conditions, with or without the shaft-driven generator connected to the load. Dynamic vibration torque measurements are also taken on a 16100TEU ship for the propulsion shaft system to analyze the consistency between simulation results and experimental results. The results show that at the rated speed of the main engine at 80 rpm and adjacent speeds, the error between the simulation calculation results and the actual measured torque results at the pre- and post-motor measurement points is less than 10% and is much less than the continuous allowable torque of 4.01 × 10⁶ N·m and the instantaneous torque. This installation state, including the propulsion shaft system with the shaft-driven generator supported by bearings, can safely navigate during normal operation. This provides theoretical and experimental support for the future installation of the propulsion shaft system with the shaft-driven generator supported by bearings. In addition, the actual ship experiment enhances the universality and reliability of the research.

A combination of Fourier cosines series and polynomials (4 terms, 4th order) in Rayleigh–Ritz method is proposed to solve the vibration problem of a generally restrained beam. The characteristics of auxiliary polynomials, which actually are determined by homogeneous boundary conditions of the beam under consideration, can directly change the convergence properties and numerical instabilities of vibration results significantly. Fast convergence and reliability of the proposed polynomials are illustrated with numerical examples in comparisons with available results.

In research concerning the impact resistance characteristics of ship power transmission shaft systems incorporating a high-elasticity coupling, a significant challenge lies in ascertaining the displacement compensation metrics for the high-elasticity coupling. This study constructs a finite element model of the ship power transmission shaft system with an entity equivalent model of the high-elasticity coupling. Utilizing the Dynamic Design Analysis Method (DDAM) and the time-history method, the dynamic responses of the high-elasticity coupling, the propulsion shaft system, and its critical cross-sections under explosive impact loads are analyzed. The findings indicate that the maximum impact displacement of the propulsion shafting system, as calculated by DDAM, is 22.47 mm in the vertical direction at the driven end of the high-elasticity coupling. In contrast, the maximum impact displacement determined by the time-history method is 15.23 mm in the same direction. The study corroborates the precision of the high-elasticity coupling equivalent model establishment methodology and confirms that the entity equivalent model of the power transmission shaft system with a high-elasticity coupling is capable of fulfilling the criteria for a swift evaluation of impact resistance characteristics. This provides theoretical backing for the forecasting of impact resistance performance in ship propulsion shaft systems.

The objective of the paper is to propose the empirical formulas of the entrained water effect based on numerical method to estimate the virtual mass and the virtual moment of inertia for tandem propellers. The fluid-solid interaction of combined propellers in the flow field has been taken into consideration in the calculation. The axial added mass and the added moment of inertia of the entrained water are calculated for a single propeller using the finite element method and the existing empirical formulas to verify the feasibility and accuracy of numerical method. Consequently, the numerical calculation of tandem propellers is conducted to obtain the novel empirical formulas of entrained water properties, which are available to evaluate the influence of the blade diameter, the expanded area ratio and the pitch/diameter ratio. The corresponding correction coefficients in the empirical formulas considering the entrained water effect of tandem propellers are given. The empirical formulas are beneficial to relevant practical engineering calculation of entrained water properties for combined propellers.