# Surface Roughness Analysis in the Hard Milling of JIS SKD61 Alloy Steel
## 4 Results and Discussion
### Interaction Effect of Factors on Response Surface  
To clearly understand the interactive influence of independent variables on the response, the 3D surface plots of the \(Ra\) are produced based on Equation (8). These graphs are generated according to the change of two factors while remaining factors are seen as a constant, and it is held in the middle level. All plots for the response surface are shown in Figure 8.  
Figure 8a indicates the interactive influence of cutting speed (\(V\)) and depth of cut (\(a\)) on the \(Ra\), for feed rate of 0.02 mm/tooth and material hardness of 45 HRC. This influence is statistically significant (see Table 5). Study of Figure 8a, it shows that the decreasing depth of cut and increasing speed lead to a remarkable decrease in the \(Ra\). This finding is similar to the results achieved by other authors. For instance, [PERSON] _et al._[7] optimized the surface roughness during hard turning of AISI H11 steel with TiN coated mixed ceramic insert by RSM. They concluded that an increase in cutting speed leads to a reduction in the \(Ra\). [PERSON] _et al._[28] predicted the surface roughness in milling process using an evolutionary programming method. They used cutting parameters such as cutting speed, feed and depth of cut to predict the surface roughness. Their results showed that the best surface roughness was always obtained at high cutting speed. This can be explained by the fact that when machining at low speeds, the built-up edge (BUE) is formed on the cutting edge of the tool and will clearly affect the  
Figure 7: Plot of residuals for surface roughness. (**a**) Normal probability plot of the residuals, (**b**) residuals versus the fitted values, (**c**) histogram of the residuals, (**d**) residuals versus the observation order. rough surface. However, when the speed is elevated, the BUE breaks away from the cutting edge and hence the machined surface quality becomes better [29]. Moreover, when milling at high cutting speed and low depth of cut, it can cause increased cutting temperatures in the shear zone. This phenomenon will produce a softer workpiece and the chip will be formed easily as a result, so it leads to better surface finish, as reported by [PERSON] _et al._[30]. Figure 8b specifies the estimated surface roughness in relation to feed rate (\(f\)) and material hardness (\(H\)), for a cutting speed of 50 m/min and depth of cut of 0.4 mm. From this figure, it can be inferred that the \(Ra\) rapidly increases with a corresponding rise in feed rate and material hardness from lower to higher values. It can be explained by the helicoidal movement of tool in machining producing the furrows on machined surfaces. If the feed rate (\(f\)) increases in the machining process, the furrows on machined surface will be deeper and broader [31]. [PERSON] _et al._[32] analyzed surface roughness in hard machining of Ti-6 Al-4V alloy using PCD (Polycrystalline diamond) tool under different coolant strategies. They concluded that as machining at an increased feed rate, it causes an increase in surface roughness due to less available time to conduct the heat from the machining region, a high material removal rate and an accumulation of chip between the workpiece-cutting tool regions. [PERSON] _et al._[33] analyzed the effect of tool edge preparation on workpiece surface integrity when turning of Ti-6 Al-4V alloy. They also indicated that as machining at high feed rate, it results in an increase in surface roughness due to generation of more distinct feed marks. Figure 8c indicates the influence of depth of cut (\(a\)) and material hardness (\(H\)) on the \(Ra\), for cutting speed of 50 m/min and feed rate of 0.02 mm/tooth. This plot shows that the surface roughness increases considerably as depth of cut and material hardness increase from lower to higher values. This can be understood that for high material hardness, acceleration of depth of cut provide a chip load which results in an increase in the observable cutting force employed.