Study of the Hull Structural Deformation Calculation Using the Matrix Displacement Method and Its Influence on the Shaft Alignment

Abstract

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.

A Pi-Theorem-Based Advanced Scaling Methodology for Similarity Assessment of Marine Shafting Systems

“…In that particular case study of the shafting system of an 82000 DWT bulk carrier, the initial alignment of the vessel was compared against the performance corresponding to different bearing offset combinations. Similar studies have been recently reported by other researchers especially focusing in the important effect of hull structural deformations in regard to shaft alignment [12][13][14].…”

Experimental Study on the Effect of Hull Deformation on the Relative Attitude between Shaft and Bearing

“…Three bearings' offset values under various conditions have been measured. The bearing reaction force can be calculated based on the offsets using the procedure described in [11]. Table 9 displays the bearing reaction forces.…”

“…The effect of rigid body displacement on shaft alignment is negligible, and it is not necessary to account for it in the testing procedure. Elastic deformation displacement refers to the global and local deformation resulting from changes in internal and external loads in the hull coordinate system [11]. Global deformation typically refers to the flexural deformation of the hull as an elongated thin-walled beam, whereas local deformation is the deformation of the local structure near the bearing as a result of the change in local pressure on the plate.…”

“…The key to analyzing the effect of ship deformation on shaft alignment is to determine the bearings' offset and rotation. Zhou [11] pointed out that the bearing offset influences the bearing reaction force, and the bearing rotation angle influences the distribution of bearing pressure. In the current state of the art, the rotation of the bearings is frequently ignored, and the influence of bearing offset on shaft alignment is given more consideration.…”

“…This method only considers the global deformation of the hull. Zhou [11] divided the hull deformation influencing the shaft alignment into global and local deformations and calculated the local deformation of the bearings using the grillage beam model. However, these methodologies have not been validated by comparing them with actual ship tests.…”