## 3 Results and Discussions  
### Effects of Focal Position on Kerf Width  
An earlier study showed that during the laser cutting of stainless steel, the cutting quality is improved when the focal position is located further inside the material [33]. However, because the study was not conducted in an underwater environment, we examined the effect of the focal position during underwater laser cutting. When the focal position was located near the front surface of the specimen, non-cut or poor cutting surfaces were obtained; when the focal position was located too far inside the material, the cutting experiments were impossible to perform owing to interference from the optical system equipment.  
Figure 3: Schematic diagram of underwater laser cutting process.  
Therefore, in this study, we compared the characteristics of underwater laser-cut specimens at focal positions of \(-20\) mm and \(-30\) mm.  
Figure 4 shows the cross-section and the cutting surface of specimens for different focal positions. Based on a comparison of the ker widths, the \(-20\) mm focal position led to a narrower front-surface kerf and a wider rear-surface kerf than the \(-30\) mm position. Under the \(-20\) mm condition, the focal position was located closer to the front surface of the specimen than it was under the \(-30\) mm condition; this resulted in a relatively smaller laser beam diameter irradiating the specimen, and consequently, a narrower front-surface kerf. However, owing to the narrow front-surface kerf, the assist gas inflow was restrained, and the molten metal discharge was stagnant; this resulted in excessive quantities of molten material, particularly near the depth of focus, which increased the temperature inside the material and widened the rear-surface kerf. In addition, the maximum thickness of the melted layer formed was relatively large at the \(-20\) mm focal position. By contrast, under the \(-30\) mm condition, the laser beam diameter irradiating the surface of the specimen became relatively larger, resulting in a wider front-surface kerf. This facilitated the inflow of assist gas and the discharge of molten metal, resulting in less melting at the depth of focus and a narrower rear-surface kerf. Consequently, the taper value, which indicates the difference between the front- and rear-surface kerf widths, decreased for the \(-30\) mm focal position.  
Based on a comparison of the drag lines for the two conditions, an appropriate drag line was formed in the upper area of the cutting surface, where melting by the laser beam was dominant for the \(-20\) mm focal position, owing to the previously mentioned reasons; however, an unstable drag line was formed in the middle, and a rough cutting surface was formed at the lower area. By contrast, for the \(-30\) mm focal position, the drag line in the upper area became longer owing to the unhampered discharge of molten metal, and a generally satisfactory cutting surface was formed.  
Figure 4: Cut cross-section and cutting surface of specimens according to the focal position; (a)\(f_{\rm d}=-20\) mm, (b)\(f_{\rm d}=-30\) mm (Processing conditions: \(P=9\) kW, \(v=30\) mm/min, \(d_{\rm N}=3\) mm, \(P_{\rm G}=10\) bar, Nozzle type = Normal plate).  
When the front- and rear-surface kerf widths, taper values, and cutting surface shapes were all considered, the cutting quality achieved with the \(-30\) mm focal position was superior.