## 5 Conclusions  
This paper employs the classic lumped-parameter equivalent system model and the Newmark-\(\beta\) step-by-step integration method to conduct dynamic response simulation calculations and experimental verification on the 16000 TEU container ship's low-speed diesel engine propulsion shaft system with a shaft-driven generator. The vibration torque amplitude on the propulsion shaft system was obtained. Through the comparison and analysis of the simulation and experimental results, the following conclusions were drawn:  
1. After the installation of the shaft-driven generator with or without bearing support, the measured torque at the pre- and post-generator measurement points in the propulsion shaft system is less than 10% different from the results of dynamic response simulation calculations, confirming the consistency between simulation results and actual ship experimental results. This further verifies the accuracy of the lumped-parameter system theoretical model of the propulsion shaft system with the shaft-driven generator.
2. Based on the actual ship experimental data, the theoretical calculation model is further calibrated, and the empirical coefficients in the calculation formula for the diesel engine excitation are revised to improve the accuracy of the simulation calculations.
3. Under normal operating conditions, the measured torque results at different measurement points are far less than the continuous allowable torque of 4.01 \(\times\) 10\({}^{6}\) N\(\cdot\)m and the instantaneous torque. This confirms that the installation of the shaft-driven generator without bearing support has a minimal impact on the dynamic response of the propulsion shaft system. The dynamic torque amplitude is within the allowable range, further indicating that the propulsion shaft system with the shaft-driven generator without bearing support can safely operate within the working speed range. This provides theoretical and experimental support for the future installation of the propulsion shaft system with the shaft-driven generator without bearing support.  
Conceptualization, methodology, investigation, writing--original draft, and writing--review and editing, [PERSON]; conceptualization, methodology, formal analysis, investigation, and writing--original draft, Z.M.; resources, supervision, funding acquisition, and validation, [PERSON]; conceptualization, methodology, formal analysis, J.W.; formal analysis, validation, L.D. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the High-Tech Research and Development Program: development of high-ice-class propulsion and manipulation systems for polar regions (project number: K24532-1-2); the funder is [PERSON].  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
Author [PERSON] was employed by the company Shanghai Marine Diesel Engine Research Institute. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Dynamic Torque**} & **Torque Amplitude** & **Torque Difference** \\  & **(kNm)** & **Ratio (\%)** \\ \hline simulation torque & 153.48 & - \\ the midpoint of intermediate shaft torque & 154.26 & 0.06 \\ rear end of motor torque & 161.17 & 4.77 \\ the front end of the motor torque & 145.42 & 5.54 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Simulation calculation results and experimental results (with shaft-driven generator connected to load).