# Surface Roughness Analysis in the Hard Milling of JIS SKD61 Alloy Steel
## 2 Experimental Details
### Identification of Cutting Conditions for the Hard Milling Test  
In this study, the cutting conditions for the hard milling test were chosen based on the structural dynamic analysis of a machine tool. The dynamic analysis of the machine tool was performed by use of CUTPRO 9.0 software, 2012. CUTPRO is advanced machining software, which is produced by the Manufacturing Automation Laboratories Corporation in B.C., Canada [18]. It can provide a high efficiency solution for the metal machining field. The procedure of structural dynamic analysis of the machine tool is shown in Figure 1.  
First step, the measurements of the machine tool dynamics were carried out by tap testing (hammer test) as illustrated in Figure 2.  
Figure 1: Illustrations of the cutting condition selection. From Figure 2, it can be seen that the structural dynamics in both the \(X\) and \(Y\) directions were measured through the Kistler 9722A2000 Hammer (2.13 mV/N sensitivity) and the 8778A500 M14 Accelerometer (10 mV/g sensitivity) (Kistler Group, Winterthur, Switzerland). The cutting tool was clamped on the machine's spindle head to carry out the various measurement tasks involved. The accelerometer was mounted on the relief face of the cutter by using a special wax. The output of the accelerometer and the hammer were connected to a PC system. During tap testing, the frequency response functions (FRF) of the structure were measured in two directions by use of the versatile transfer function measurement program in CUTPRO software, which was installed in a PC system. In the second step, a small series of slotting milling tests were conducted at different feed rates, but constant spindle speed and depth of cut. Furthermore, this study was performed on the hardened JIS SKD61 steel with hardness in the range of (40-50) HRC. Therefore, to ensure machinability, the material which had the highest hardness among given materials was selected to calculate the average cutting force coefficients. With this approach, the input parameters of the average cutting coefficient tests were listed in Table 1[19]. The procedure of slotting milling tests was shown in Figure 3.  
The cutting force components in three directions were measured utilizing a piezoelectric three-component Dynamometer with Model 6423 (Lebow(r) Products Inc., Troy, MI, USA) and a \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test** & **Spindle Speed, \(n\) (rpm) & **Feed Rate, \(f\) (mm/Tooth) & **Axial Depth of Cut, \(a\) (mm) & **Hardness, \(H\) (HRC)** \\ \hline
1 & 850 & 0.050 & 0.3 & 50 \\
2 & 850 & 0.075 & 0.3 & 50 \\
3 & 850 & 0.100 & 0.3 & 50 \\
4 & 850 & 0.125 & 0.3 & 50 \\
5 & 850 & 0.150 & 0.3 & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental conditions for calculating the average cutting force coefficients. Figure 3: Experimental configuration for identification of cutting force coefficients. Figure 2: Dynamic parameter measurement of machine tool. System 6000's with Model 6100 scanner (Vishay Precision Group, Inc., Atlanta, GA, USA) connected to a PC employing Strain Smart force measurement software. A digital filter which was designed based on the fast Fourier transform algorithm was integrated into the System 6000 to filter out the noise signal during the measurement. For each machining condition, 1000 data points for each of the three channels were recorded by sampling at 1000 Hz for a period of 1 s.  
The modeling of average cutting force coefficients was shown in Equation (1) [15]. \[ \begin{array}{l}K_{tc}=\frac{4\overline{F_{vc}}}{Na};\;K_{rc}=\frac{-4 \overline{F_{vc}}}{Na};\;K_{ac}=\frac{\pi\overline{F_{vc}}}{Na}\\ K_{te}=\frac{\pi\overline{F_{vc}}}{Na};\;K_{re}=\frac{-\pi\overline{F_{vc}}}{Na}; \;K_{ae}=\frac{2\overline{F_{vc}}}{Na}\end{array}