## 5 Alignment Optimization
### Response Surfaces of the Dynamic BLINs
It can be found from Figure 8e,f that the load characteristics between the stern bearings and the thrust bearing are highly coupled. The displacements of the stern bearings, especially for the front stern bearing, significantly influence the load of the thrust bearing, making the BLINs transit from positive to negative within a small displacement range. Therefore, the variation law of the influence number of the thrust bearing about itself \(A_{33}\) was further analyzed, as shown in Figure 9.  
According to Figure 9a, when \(\Delta y_{3}=-2\) mm, \(A_{33}\) changes linearly with \(\Delta y_{1}\). With the increase in \(\Delta y_{3}\), the decreasing amplitude of \(A_{33}\) with the elevation of the rear stern bearing increases significantly, indicating an obvious positive coupling between \(\Delta y_{1}\), \(\Delta y_{3}\) and the load of the thrust bearing. According to Figure 9b, when \(\Delta y_{3}=-2\) mm, \(A_{33}\) decreases significantly with the increase in \(\Delta y_{2}\). With the increase in \(\Delta y_{3}\), the decreasing amplitude of \(A_{33}\) with the elevation of the front stern bearing decreases significantly, indicating an obvious negative coupling between \(\Delta y_{2}\), \(\Delta y_{3}\) and the load of the thrust bearing. With the variation in \(\Delta y_{2}\) and \(\Delta y_{3}\), the maximum value of \(A_{33}\) is 56.2 kN/mm, suggesting that the amplification effect of the coupling of \(\Delta y_{2}\) and \(\Delta y_{3}\) on \(A_{33}\) is bigger than that of \(\Delta y_{2}\) alone. The displacement of the front stern bearing will lead to an obvious load change of the thrust bearing. From the analysis above, it can be seen that the BLINs of the thrust bearing demonstrate high sensitivity to the displacement of each bearing. The displacement of the thrust bearing has a strong nonlinear relationship with the displacements of the stem bearings. Therefore, during alignment optimization, it is necessary to focus on the load of the thrust bearing and avoid large displacement of the thrust bearing to avert safety threats caused by uneven load distribution among the bearings. In order to intuitively reflect the relationship between bearing loads and bearing displacements, some of the response surfaces between bearing reaction forces and bearing displacements are shown in Figure 10.  
In Figure 10a-c, when \(\Delta y_{3}\) is a constant value, the reaction force of the rear stern bearing \(F_{1}\) initially decreases and then increases with the elevation of the rear stern bearing. When \(\Delta y_{1}\in[-3.5,0]\) mm, \(\Delta y_{3}\in[-2,0]\) mm, the load is mainly on the front stern bearing. When the vertical position of the rear stern bearing is elevated, due to the large load influence numbers of the thrust bearing, the load of the rear stern bearing initially decreases and then increases. Meanwhile, the load of the front stern bearing decreases and that of the thrust bearing increases. When \(\Delta y_{1}\in[0,3.5]\) mm and \(\Delta y_{3}\in[0,2]\) mm, elevating the rear stern bearing and the thrust bearing will increase the load of themselves, but reduce the load of the front stern bearing. When \(\Delta y_{3}=2\) mm, the load of the thrust bearing increases initially and then decreases with the elevation of the rear stern bearing. This is because when \(\Delta y_{1}\in[0,2]\) mm, the raft frame is still middle arched, and enlarging \(\Delta y_{1}\) will significantly reduce the load of the front stern bearing. The load reduction in the thrust bearing caused by elastic deformation is less than the load increase caused by the BLINs, making the load of the thrust bearing increase initially and then decrease. From Figure 10d, it can be seen that excessive vertical displacements of both the front stern bearing and thrust bearing will reduce the load of the rear stern bearing.