# Forming Difficulty Evaluation for Curved Hull Plates Based on Grey Relational Analysis
## 2 Analyze the Influence Law of Forming Difficulty of Complex Curved Hull Plates  
Double curved plates at the bow and stern of the real ship are shown in Figure 1. Figure 2a shows the line heating forming process in the shipyard, which is divided into a heating stage and a cooling stage. As shown in Figure 2b, the heat source is preheated for 5 s at the initial position of the heating line. The heat source moves along the heating direction at a certain velocity, and the cooling water moves with the heat source at the same velocity. The distance between the heat source and cooling water is 0.15 m. When the heat source moves to the end of the heating line, water cooling is applied to the whole plate surface.  
Figure 1: Double curved plates at the bow and stern of real ships: (**a**) bulbous bow; (**b**)stern.  
Figure 2: Line heating forming process: (**a**) actual forming process; (**b**) heating and cooling stage.  
During the heating stage, the surface of the steel plate is heated by a heat source, which causes the plate to expand. Uneven thermal stress is generated due to the temperature gradient in the thickness direction of the plate. The surface temperature of the steel plate rapidly decreases under the action of cooling water, which leads to the shrinkage of the plate.  
The mechanism analysis of the expansion and shrinkage is shown in Figure 3a,b. The shrinkage is generated near the heating line during the line heating process. According to the actual forming experience, five pairs of measuring points are set at the position of 0.05 m away from the heating line on both sides of the heating line as shown in Figure 3b. The measuring points are marked by marking tools. The distance between the points of each group is measured by a digital caliper before and after line heating. The difference between the measured data before and after forming is the shrinkage. The shrinkage in the cooling stage is greater than the expansion in heating stage. Figure 4 shows the formed double curved plate.  
There are many factors affecting the forming difficulty of complex curved hull plates [14], which can be divided into plate geometry parameters, forming parameters, etc. In order to evaluate the difficulty of line heating of complex outer hull plates, the factors that influence the deformation during the forming of water fire bending plates are studied, including plate length, plate width, plate thickness, radius of curvature, heating speed, heating line length, heating line spacing and the difference in the heating line number on both sides of the curved plate. The correlation between the influencing factors and the forming difficulty of curved hull plates is studied.  
Figure 3: Schematic diagram of deformation in line heating: (**a**) deformation of plate cross-section; (**b**) measurement points for shrinkage.  
The difficulty of forming complex curved hull plates is mainly reflected in the deflection deformation. Deflection refers to the overall deflection, which is the distance from the point of maximum curvature of the curved plate to the line connecting the end points on both sides of the curved plate. The sketch map and forming experiment of line heating are shown in Figure 5. The deflection is measured by displacement sensor. The displacement sensor is connected with the computer to measure the deflection of the monitoring point in real time. Under the same forming conditions, the greater the deflection deformation of the curved plate, the lower the forming difficulty of the curved plate. In the previous research [15], a numerical model for deflection calculation is established, whose calculation results is verified by experimental comparison. Based on the existing data model, the influence law of different influencing factors on deflection deformation is studied. Then the influence laws of different influencing factors on the forming difficulty of complex curved hull plate are obtained.