## 2 Optimization of MQL Parameters  
### Experimental Procedure  
In the first part of the research, the air pressure, the fluid flow, and a different lubricant of MQL conditions were optimized to obtain improved cutting performances in the hard milling process with consideration of surface roughness. The Taguchi method is widely used because it is a simple and robust method used to optimize the parameters of the process involving a significant reduction in cost and processing time [23]. In the experimental design, the Taguchi method uses the orthogonal arrays to obtain the best results with a minimum number of experiments. A signal to noise (\(S/N\)) ratio is used to measure the performance characteristics and to calculate the percent contribution of each process parameter by analysis of variance. The \(S/N\) ratio represents the amount of variation present in the quality characteristic in which the term \(S\) represents the mean value for the output characteristic, and the \(N\) represents the undesirable value for the output characteristic. The analysis of the \(S/N\) ratio could be classified into 3 types: the-bigger-is-the-better, the-smaller-is-the-better, and the-nominal-is-the-better [23; 24]. Thus, the appropriate type is selected for each specific case. The purpose of this study is to optimize the parameters of the MQL condition to get the better surface roughness available. Therefore, the-smaller-is-the-better type was selected. It is calculated according to the following formula:  
\[\frac{S}{N}=-10\text{log}\frac{1}{n}(\sum_{i=1}^{n}y_{i}^{2}) \tag{1}\]  
where: \(y_{i}\) is the observed data, \(n\) is the number of experiments which are repeated. With three parameters at three levels, [PERSON]\({}^{\prime}\)s L9 orthogonal array was used to organize the experiments. The parameters with three levels of the MQL as the fluid flow, pressure, and lubricant are shown in Table 1. The lubricant factor includes straight cutting oil, vegetable oil, and water-soluble oil. Straight cutting oil and water soluble oil have been proved highly effective in industrial production. Vegetable oil has been used and proven to be effective in a number of recent studies [7; 8]. The air pressure factor includes 3, 4, 5 kg/cm\({}^{2}\). This range has been commonly applied in industry. The range of fluid flow factor is from 10 to 50 mL/h. The selected range of fluid flow is near dry condition. The milling process information is shown in Table 2. The details of the milling tool are given in Table 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Level 1** & **Level 2** & **Level 3** \\ \hline Lubricant & Straight Cutting Oil & Vegetable Oil & Water-Soluble Oil \\ Fluid flow (mL/h) & 10 & 30 & 50 \\ Pressure (kg/cm\({}^{2}\)) & 3 & 4 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters and levels. The milling process of the AISI H13 steel was performed by a Victor V-Center-4 Vertical Machining Center (Victor Taichung Machinery Works Co., Ltd., Taichung, Taiwan). The hardness of the workpiece is 50 HRC. The tool used is a \(\upi\)10 TiAlN coated end mill of the CMTec Company (Tainan, Taiwan). All the tests were conducted under a cutting condition fixed as cutting speed \(v\) = 55 m/min, feed rate \(f\) = 0.02 mm/tooth and depth of cut \(d\) = 0.6 mm. The cutting parameters were selected based on workpiece material, tool material, hardness of workpiece, and the CMTec cutting tool company's recommendation. The NC code was created for the CNC machine by use of Mastercam X software (Version 10, CNC Software, Inc., Tolland, CT, USA, 2005). The details of the experiment performed with a nozzle position in relief face of the tool as fixed for all experiments is illustrated in Figure 1. This position has high lubrication performance due to the lubricant's facile penetration of the cutting zone. The surface roughness was measured by use of the SJ-401 surf-test instrument manufactured by the Mitutoyo Corporation (Kawasaki, Japan).