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 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.

The pressure distribution of a misaligned elastomeric journal bearing is crucial for analyzing the uneven excessive wearing of the propulsion shaft bearing. However, analysis of the misaligned bearing is usually mainly based on the finite element method (FEM), which lacks a convenient and effective calculation method. This paper uses the influence coefficient factors (ICs) method to analyze the contact pressure of the misaligned bearing. First, the elastic displacement of the cylindrical shell subjected to a single point of concentrated force is derived and used to attain the new influence coefficient factors. Then, the geometric boundary conditions of planar conformal cylindrical contact are extended to the case of non-planar contact. Finally, the proposed method is applied and compared with other methods. The results show that the influence coefficient factors are greatly affected by the shape and constraints of the contact object. The proposed method is suitable for cylindrical shell contact analysis and has the same accuracy as FEM with half of the time consumption. In addition, the bearing capacity and contact stiffness are decreased as the effective contact area decreases due to misalignment.