Effects of Aft Stern Bearing Installation Errors on Ship Shaft Alignment: A Three-Moment-Equation Sensitivity Analysis

Local installation errors in stern-tube bearings can substantially affect shaft alignment, yet conventional calculations often represent these errors only as nominal support displacements. This study extends the three-moment-equation framework by explicitly parameterising vertical and lateral offsets of the aft stern bearing within the compatibility equations for a multi-supported shaft beam. The method is benchmarked against published bearing-elevation data. Relative to the reference calculation, the mean absolute error (MAE) and root-mean-square error (RMSE) are 0.043 and 0.055 mm, respectively; relative to the reported installation elevations, the corresponding values are 0.229 and 0.281 mm. The method is then applied to the shafting system of a large container ship to evaluate changes in shaft deformation and slope, bearing clearance, maximum pressure, bearing load, shear force, bending moment, and support stiffness. For this case, the vertical offset is the dominant disturbance: an increase from 0 to 0.1 mm raises the maximum aft-bearing pressure by 12.19% and reduces its support stiffness by 14.39%. The effects of lateral offset remain limited up to 0.3 mm, whereas a secondary contact region develops at approximately 0.4 mm. This transition is case-specific and should not be interpreted as a universal tolerance limit. The method is intended as a rapid preventive tool for assessing installation tolerances; however, its pressure and stiffness predictions require further validation of the contact model and additional experimental evidence.