# Surface Roughness Analysis in the Hard Milling of JIS SKD61 Alloy Steel
## 2 Experimental Details
### Identification of Cutting Conditions for the Hard Milling Test
 \tag{1}\]  
where \(K_{tc}\), \(K_{rc}\), \(K_{ac}\) are cutting coefficients of the tool/workpiece material pairing in tangential, radial and axial directions (N/mm)\({}^{2}\); \(K_{te}\), \(K_{ae}\) are edge cutting coefficients of the cutting tool in tangential, radial and axial directions (N/mm); \(N\) is the number of teeth on the cutter; \(a\) is depth of cut; \(\left(\overline{F_{xc}},\;\overline{F_{yc}},\;\overline{F_{zc}}\right)\) and \(\left(\overline{F_{xc}},\;\overline{F_{yc}},\;\overline{F_{zc}}\right)\) are average cutting forces and average edge cutting forces in three directions respectively (Newton). The average cutting force coefficients were calculated from the measured cutting force data obtained through the use of the CUTPRO software. After calculating, the average cutting force coefficients are given in Table 2.  
For the third step, once the FRFs and the cutting constants were determined, these data were used in the CUTPRO software to make the stability lobe diagram, as shown in Figure 4. This diagram was produced using Equation (2) [15]. \[a_{\text{lim}}=-\frac{2\pi\Lambda_{R}}{NK_{t}}\left(1+\kappa^{2}\right) \tag{2}\]  
where \(a_{lim}\) is chatter-free axial depth of cut; \(N\) is the number of teeth on the cutter; \(K_{t}\) is the cutting force coefficient; \(\kappa=\Lambda_{R}/\Lambda_{I}\); \(\Lambda_{R}\) and \(\Lambda_{I}\) are the real part eigenvalue and the imaginary part eigenvalue of the chatter stability equation. From Figure 4, it was seen that the chatter stability lobes create a spindle speed-dependent dividing line between the unstable and stable depth of cut. These stability lobes can be used to find the best machining parameters for the measured machine tool system. Figure 4: Analytical stability lobe diagram of the hard milling test. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Cutting Coefficients**} & \multicolumn{4}{c}{**Edge Cutting Coefficients**} \\ \hline \(\mathbf{K_{tc}}\) **(N/mm\({}^{2}\))** & \(\mathbf{K_{rc}}\) **(N/mm\({}^{2}\))** & \(\mathbf{K_{ac}}\) **(N/mm\({}^{2}\))** & \(\mathbf{K_{te}}\) **(N/mm)** & \(\mathbf{K_{re}}\) **(N/mm)** & \(\mathbf{K_{ae}}\) **(N/mm)** \\ \hline \(-654.089\) & \(-2868.340\) & \(645.043\) & \(-66.743\) & \(-89.743\) & \(13.832\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average cutting coefficients of JIS SKD61 (50 HRC). Finally, the spindle speed and the axial depth of cut in a stable cutting region were selected based upon the chatter stability lobe diagram. From this diagram, the cutting speed (\(V\)) in the range of 25-75 m/min and the depth of cut (\(a\)) in the range of 0.2-0.6 mm were selected for investigation. Moreover, the present work focused on the study of finish milling of hardened JJS SKD61 alloy steel with hardness in the range of (40-50) HRC. All the experiments were conducted by slotting milling operation. Thus, the best feed rates were often chosen in the range of 0.01-0.03 mm/tooth. The radial depth of cut was seen as a constant that is equal to the diameter of the cutting tool (\(d\) = 10 mm). With this approach, the selected cutting condition parameters for hard milling of hardened JJS SKD61 alloy steel are shown in Table 3.