Prediction of Equivalent Pivot of Stern Bearing with Inclined Shaft and Iterative Alignment of Shafting

To address the limitations of mechanical modeling of the stern bearing in the alignment of ship propulsion shafting, the prediction of the equivalent fulcrum of the stern bearing of the ship was studied with consideration of the shaft inclination and the iterative alignment of the shafting. The Reynolds and film thickness equations of hydrodynamic lubrication were established based on the inclination of the journal of the stern bearing. According to the principle of moment balance and numerical calculation, the solution formula for the position of the equivalent fulcrum of the stern bearing was obtained. Using journal inclination angle, aspect ratio, and external load as variables, the inclination angle, aspect ratio, and external load effects on the position of the equivalent fulcrum were analyzed. Data fitting was used to construct the estimated calculation formula of the equivalent fulcrum position. The findings show that the equivalent fulcrum position prediction formula has high precision, with position error of the equivalent fulcrum obtained by numerical analysis not more than 3.7% and average error of −1.7%. Finally, an iterative alignment method for shafting was established with three bending moments combined with equivalent fulcrum estimation. To test the method, the calibration calculation of the propulsion shafting of a new ship was carried out. The new method was used to calculate the support and reaction force of the stern bearing with propeller immersion proportions of 0%, 50%, 75%, or 100%. Compared with the shipyard calibration report, the calculated results of the stern bearing support reaction force under different propeller immersion using this method were reduced by an average of 5% and the inclination angle was reduced by an average of 8%.