# Surface Roughness Analysis in the Hard Milling of JIS SKD61 Alloy Steel
## 4 Results and Discussion
### Optimization for Ra  
The objective of this research is to find the optimal values of input parameters that minimize \(Ra\) when hard milling of JIS SKD61 alloy steel with a coated carbide tool. To solve this problem, the single objective optimization is conducted based on the desirability function. The input parameters, the goals, the limits and the weight are completely listed in Table 6. The results of optimization for the \(Ra\) are illustrated in Figure 9 and are also summarized in Table 7. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Conditions** & **Goal** & **Lower Limit** & **Target** & **Upper Limit** & **Weight** \\ \hline \(V\) (m/min) & Is in range & 25 & - & 75 & - \\ \(f\) (mm/tooth) & Is in range & 0.01 & - & 0.03 & - \\ \(a\) (mm) & Is in range & 0.2 & - & 0.6 & - \\ \(H\) (HRC) & Is in range & 40 & - & 50 & - \\ \(Ra\) (\(\mu\)m) & Minimum & 0.205 & 0.205 & 0.588 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Constrains and goals for single objective optimization. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Resposes** & \multicolumn{4}{c}{**Optimum Conditions**} & \multicolumn{2}{c}{**Predicted Value**} & \multicolumn{2}{c}{**Experimental Value**} & \multicolumn{1}{c}{**Error (\%)**} \\ \hline \(Ra\) (\(\mu\)m) & 75 & 0.01 & 0.2 & 40 & 0.118 & 0.122 & 3.2 \\ \hline \multicolumn{8}{c}{Desirability = 1.} \\ \end{tabular}
\end{table} 
Table 7: The results of the optimization for responses. Figure 9: Single objective optimization plot. Table 7 shows that the optimized milling parameters for minimizing \(Ra\) are cutting speed of 75 m/min, feed rate of 0.01 mm/tooth, depth of cut of 0.2 mm, a material hardness of 40 HRC and an optimized surface roughness value of 0.118 \(\upmu\)m. Moreover, the desirability value is 1 as reported in Table 7. It could be reasonably concluded that the desirability function approach is very suitable for optimizing \(Ra\) in machining operations. Once the optimum machining parameters are determined, the validation experiments need to be carried out to verify the accuracy of the obtained model. The valid result, as shown in Table 7, reveals that the obtained surface roughness \(Ra\) under the optimized machining parameters (_i.e._, \(V\) = 75 m/min, \(f\) = 0.01 mm/tooth, \(a\) = 0.2 mm and \(H\) = 40 HRC) is 0.122 \(\upmu\)m. The percentage error between measured and predicted values of \(Ra\) is 3.2%, which is found to be insignificant. Therefore, the RSM method is considered to be suitable for optimization of surface roughness in the hard milling process of JIS SKD61 steel. A relative comparison was conducted with other authors. [PERSON] _et al._[3] optimized the cutting conditions for surface roughness during milling of AISI H13 hardened alloy steel (equivalent to JIS SKD61 steel). They indicated that the depth of cut was the most influential parameter on the surface roughness. Under the optimized cutting conditions, the surface roughness was less than 0.25 \(\upmu\)m. [PERSON] _et al._[4] achieved about 0.8 \(\upmu\)m surface roughness value in the toroidal milling of hardened SAE H13. [PERSON] _et al._[30] obtained 0.19 \(\upmu\)m surface roughness value when milling Ti-6 Al-4V ELI alloy. They reported that the feed rate and depth of cut have the greatest influence on surface roughness. [PERSON] _et al._[37] obtained less than 0.3 \(\upmu\)m surface roughness when high-speed face milling AISI H13 steel. They also indicated that the two most important factors affecting the surface roughness were the depth of cut and the cutting speed. However, [PERSON] _et al._[38] showed that the feed rate was the most effective factor among the given factors on surface roughness when high-speed milling of hardened die steel (61-62) HRC, whereas the cutting speed and the depth of cut were insignificant factors under the same parameters. The present study shows that the two significantly effective factors on the surface roughness are the feed rate and the depth of cut. This finding is similar to the result obtained from [PERSON] _et al._[30].