## 2 Experimentation Details  
The Hastelloy X bar having 20 mm diameter and 300 mm length is used for conducting the turning experiments on a C6140H turning machine. VNMG160408-SM1105 PVD TiAlN cutting tool inserts are used to do the turning operation. The impact of tool wear on the machinability indices is completely eliminated by using new inserts every time. The CF (Tangential Force, F\({}_{2}\)) is calculated with a 9257B Kistler dynamometer, and the value is manipulated with dynoware software. The workpiece surface roughness (Ra) is measured using a contact-type surface roughness tester (TR200), a cutoff length of 0.8 mm, and a traverse length of 4 mm. For measuring the CT, a FORTIC 226 infrared imaging sensor is used. Cryogenic equipment consists of a self-pressurized pump, cryogenic dewar tank capacity of 50 L. At a pressure of 0.3 bar, LN\({}_{2}\) was sprayed onto the work-tool interface using a copper nozzle diameter of 3 mm. Figure 2 depicts a schematic representation of the experimental setup. The detailed experimental conditions are shown in Table 1.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Items** & **Descriptions** \\ \hline Workpiece & Hastealloy \(\times\) (\(\Omega\)20 \(\times\) 300 mm) \\ \hline Material Properties & **Chemical Composition (\%):** Ni:50, Cr:21, Mo:17, Fe:2, Co:1,W:1, Mn:0.80, Al:0.05, Si:0.08, C:0.01, B:0.01 \\  & **Physical Properties:** Tensile strength:1370 MPa, Yield Strength: 1170 MPa, Hardness:388 HB \\ Insert Specification & VNMG160408-SM1105, PVD TiAlN coated carbide insert, Sandvick \\  & 0.8 mm \\  & \(7^{\circ},6^{\circ}\) \\  & Depth of cut (a\({}_{\text{P}}\)) & 0.1 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimental Conditions.  
Figure 2: (a) Schematic View, Experimental Setup (b) Dry (c) Wet (d) Cryogenic Machining.  
In this work, turning experiments were performed using L\({}^{3}\)\({}_{27}\) full factorial experimental design using Minitab 17. three factors are considered for this experiment: \(v_{c}\), \(f\), and environment; each factor has three different levels, as shown in Table 2.  
The experimental design and the corresponding measurement of machinability indices are presented in Table 3.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Factors** & **Unit** & **Symbol** & **Level 1** & **Level 2** & **Level 3** \\ \hline Cutting speed (\(\perm_{\text{c}}\)) & m/min & A & 33 & 87 & 124 \\ \hline Feed rate (\(f\)) & mm/rev & B & 0.05 & 0.1 & 0.15 \\ \hline Environment & & C & \(1\) & 2 & 3 \\  & & & **(Dry)** & **(Wet)** & **(Cryogenic)** \\ \hline \hline \end{tabular}
\end{table}
Table 2: L\({}^{3}\)\({}_{27}\) full factorial experimental design.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**S.no** & **Cutting Speed** & **Feed Rate** & **Environment** & **Cuting Force** & **Surface Roughness** & **Cutting Temperature** \\ \hline  & **m/min** & **mm/rev** & & **Fz (N)** & **Ra (\(\mu\)m)** & \({}^{\circ}\)**C** \\ \hline
1 & 33 & 0.05 & Dry & 256 & 3.42 & 380 \\ \hline
2 & 87 & 0.05 & Dry & 192 & 3.01 & 416 \\ \hline
3 & 124 & 0.05 & Dry & 165 & 2.98 & 472 \\ \hline
4 & 33 & 0.1 & Dry & 339 & 2.96 & 435 \\ \hline
5 & 87 & 0.1 & Dry & 281 & 2.83 & 477 \\ \hline
6 & 124 & 0.1 & Dry & 220 & 2.72 & 515 \\ \hline
7 & 33 & 0.15 & Dry & 430 & 2.75 & 510 \\ \hline
8 & 87 & 0.15 & Dry & 385 & 2.62 & 550 \\ \hline
9 & 124 & 0.15 & Dry & 322 & 2.53 & 596 \\ \hline
10 & 33 & 0.05 & Wet & 245 & 3.25 & 250 \\ \hline
11 & 87 & 0.05 & Wet & 186 & 2.86 & 313 \\ \hline
12 & 124 & 0.05 & Wet & 156 & 2.80 & 347 \\ \hline
13 & 33 & 0.1 & Wet & 302 & 2.87 & 386 \\ \hline
14 & 87 & 0.1 & Wet & 276 & 2.74 & 414 \\ \hline
15 & 124 & 0.1 & Wet & 208 & 2.68 & 472 \\ \hline
16 & 33 & 0.15 & Wet & 412 & 2.69 & 491 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Experimental design values.