## 3 Results
Figure 6 shows the main effect plots of the S/N ratios for each of the input variables. The lowest output values for each controllable variable are obtained when the S/N values are at their maximum. The trends on the S/N plots indicate that feed rate variations have the highest influence on the thrust forces and deviation of the hole. The highest S/N ratios, corresponding to the lowest thrust forces, can be obtained at a cutting speed of 40 m/min (level 1), feed rate of 0.05 mm/rev (level 1) and using CCA cooling (level 1). In terms of hole deviation, the highest S/N ratios, indicating lower hole deviations, were obtained using the highest cutting speed of 100 m/min (level 3), lowest feed rate of 0.05 mm/rev (level 1) and using the MQL cutting environment (level 2). Increasing cutting speed caused an increase in thrust forces. Observing the influence of cutting speed on built-up edge dimension, an increasing trend was noted that could be the main reason for the thrust force increase. Built-up edge length was lowest while machining at a cutting speed of 40 m/min (level 1), feed rate of 0.125 mm/rev (level 2) and using cutting fluid (level 3). Finally, the lowest built-up edge heights were obtained using the highest cutting speed tested of 100 m/min (level 3), lowest feed rate of 0.05 mm/rev (level 1) and using the MQL cutting environment (level 3), 0.05 mm/rev (level 1) and using the MQL cutting environment (level 3). Even though the S/N ratios give a good indication of how controllable factors influence the output variables, it is hard to identify a single controllable factor combination that will yield the best results. For this purpose, grey relation analysis, GRA, and statistical analysis of variance, ANOVA, were implemented in this research. The first step of the GRA involves the pre-processing of the output data. This can be calculated in two ways depending on whether lower or higher output values are preferred. In this research, reducing thrust forces, hole deviation and BUE dimensions is beneficial, which is why a \"lower-is-better\" case was selected and calculated using the following formula:  
\[\mathrm{x_{ij}}=\frac{\mathrm{max}\big{(}\mathrm{y_{ij}}\big{)}-\mathrm{y_{ij}} }{\mathrm{max}\big{(}\mathrm{y_{ij}}\big{)}-\mathrm{min}\big{(}\mathrm{y_{ij}} \big{)}} \tag{2}\]  
Figure 6: Cutting speed, feed rate and cutting environment grey relation grades. where: xij--grey relation value, yij--observed output parameter, max yij--maximum value of the observed output parameter, min yij--minimum value of the observed output parameter. After the data has been processed, grey relation coefficients can be calculated with the following formula:  
\[\xi_{\text{ij}}=\frac{\Delta_{\text{min}}\ +\zeta\Delta_{\text{max}}}{\Delta_{ \text{ij}}\ +\zeta\Delta_{\text{max}}} \tag{3}\]  
\[\Delta_{\text{ij}}\ =\left|\text{x}_{0\text{j}}-\text{x}_{\text{ij}}\right| \tag{4}\]  
\[\Delta_{\text{min}}\ =\min\left\{\Delta_{\text{ij}},\ \text{i}=1,2,\ldots,\text{m };j=1,2,\ldots,\text{n}\right\} \tag{5}\]  
\[\Delta_{\text{max}}=\max\left\{\Delta_{\text{ij}},\ \text{i}=1,2,\ldots,\text{m };j=1,2,\ldots,\text{n}\right\} \tag{6}\]  
where \(\zeta\), the distinguishability coefficient \(\zeta\in\) (0,1), was selected as 0.5. Finally, in the last step of the grey relation analysis, the grey relation grade must be calculated:  
\[\text{y}_{\text{i}}=\frac{1}{\text{n}}\sum_{\text{j=1}}^{\text{n}}\xi_{\text{ ij}} \tag{7}\]  
where: n--experiment number. Table 5 shows the grey relation coefficients and grey relation grades for each test run. The test with the highest grey relation grade indicates the closest optimal controllable parameter. The optimal parameters calculated using this method are shown in bold in Table 6. For this set of controllable factors, the lowest output parameters were achieved using the lowest cutting speed of 40 m/min, the lowest feed rate of 0.05 mm/rev using the MOL cutting environment.