Line heating is used in forming the complex curve plates of ships, and this process is becoming integrated into automated tools. Induction heating equipment has become commonly used in automatic line heating. When applying automated equipment, it is necessary to calculate the relationship between the heating parameters and the temperature field. Numerical methods are primarily used to accomplish the calculations for induction heating. This computation process requires repeated iterations to obtain a stable heat generation rate. Once the heat generation rate changes significantly, a recalculation takes place. Due to the relative position of the coil and plate changes during heating, the grid needs to be frequently re-divided during computation, which dramatically increases the total computation time. In this paper, through an analysis of the computation process for induction heating, the root node that restricts the computation efficiency in the conventional electromagnetic-thermal computation process was found. A method that uses a Gaussian function to represent the heat flux was proposed to replace the electromagnetic computation. The heat flux is the input for calculating the temperature field, thus avoiding the calculation of the electromagnetic analysis during induction heating. Besides, an equivalence relationship for multi-coil was proposed in this paper. By comparing the results of the experiment and the numerical method, the proposed heat source model’s effectiveness was verified.

The analysis of the influence of hull deformation on shaft alignment is predominately conducted using the finite element method (FEM), which is time-consuming, labor-intensive, and challenging to use for iterative hull design optimization. In this paper, hull deformation is separated into two parts—global deformation and local deformation, simplified to a single-span beam model and a grillage beam model, respectively—then solved using the matrix displacement method (MDM). Compared to FEM, the proposed method has a small calculation error, proving its correctness, while the calculation time is greatly reduced. The proposed method has been used to calculate the hull deformation of a ship under various conditions and evaluate its influence on shaft alignment. The results indicate that under certain conditions, the bearing reaction forces are constant, whereas the bearing pressure changes as a consequence of the change in shaft-to-bearing angle. The comparison between local rotation and shaft-to-bearing angle reveals that bearings in various positions follow distinct laws. We suggest that the shaft-to-bearing angle be used as an additional parameter in the evaluation of shaft alignment calculations. Moreover, when optimizing bearing pressure, bearings in different positions are affected differently by global and local deformation, and their optimization priorities are distinct.

The longitudinal vibration of the propulsion shaft system is a challenging issue for marine noise management. We conducted various static and dynamic tests on our built test rig for the shafting system, presenting the results in this paper. By combining experimental data and the particle swarm optimization algorithm, we identified the structural parameters that are difficult to obtain. With these parameters we establish a completed theoretical model of a shaft system containing branches, analyze how and why static thrust affects vibration, and give quantitative results of the force transmissibility. Our work provides a reference for subsequent researchers.

Line heating is an essential process in the formation of ship hull plates with a complex curvature. Electromagnetic induction heating is widely used in the line heating process. In electromagnetic induction heating, the shape of the coil and the air gap between the inductor and workpiece could influence the heat source distribution. Moreover, in the line heating process, the change of curvature of the plate will cause a change of the air gap of the inductor. Magnetic thermal coupling calculation is an effective method for simulating induction heating. This paper used the finite element method to calculate the distribution of heat sources in different initial plate curvatures and coil widths. The changes in heat source distribution and its laws were investigated. The results show that when the coil width is less than 100 mm, the effect of plate curvature on heat source distribution and strain distribution is not apparent; when the coil width is greater than 100 mm, the plate curvature has a visible effect on the heat generation distribution. In the case of a curvature increasing from 0 to 1 and a coil width equal to 220 mm, the Joule heat generation in the center of the heating area is reduced by up to 21%.

The unclear change laws of bearing offset and rotation, both of which influence the condition of shaft alignment during hull deformation, make it difficult to optimize shafting design. In this paper, an integrated hull-bearing-shaft model is designed and built for a cantilever beam loading test. Displacement sensors are utilized to determine the change in displacement of the hull, bearings, and shaft. The pressure distribution at the bow and stern ends of the bearing is measured using a new type of thin-film pressure sensor. The test results show that the rotation angle of the shaft and bearing varied differentially during hull deformation, and the magnitude of the shaft-bearing angle was comparable to the rotation angle. The measured rotation angles of the front and rear ends of the stern tube bearings are opposite to the theoretical value of a cantilever beam, indicating that the stern tube has a non-negligible effect on local deformation, and it is recommended to measure the bearings directly as opposed to the alternative structure to obtain the rotation. The change pattern of the shaft and bearing attitude does not change with the different initial state of the shaft, which indicates that the initial error of installation will be retained during the hull deformation process. The change pattern of the shaft and bearing attitude is unaffected by the initial state of the shaft, indicating that the initial installation error will persist during hull deformation. In some instances, the bearing reaction force remained unchanged, but the shaft-bearing angle and bearing pressure altered, indicating that the bearing condition cannot be determined solely by the bearing reaction force. The results of bearing pressure and the shaft-bearing angle can be compared, indicating that the thin-film pressure sensor can be used to determine the status of the shaft-bearing angle, particularly during the installation phase.