## 3 Results and Discussion  
### Analysis for COF and Wear Rate  
The tribological experiments with varying parameters on thrust collar tribotester were conducted, and the results of the COF and wear rate for each run are listed in Table 6. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Run Order**} & \multicolumn{2}{c}{**Actual Factor**} & \multicolumn{2}{c}{**Coefficient**} & \multicolumn{2}{c}{**Wear Rate**} \\ \cline{2-5}  & **A: Nanoparticles (wt \%)** & **B: SDS (wt \%)** & **C: Water (wt \%)** & **of Friction** & **(10\({}^{-10}\) cm\({}^{3}\)/N-m)** \\ \hline  
& 10 & 0.0514 & 8.2515 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experimental results of coefficient of friction (COF) and wear rate as per orthogonal array. The ANOVA analysis for the COF and wear rate were performed to determine the effect of main factors on the COF and wear rate, the results are listed in Tables 7 and 8. The confidence level of the predicted model was 95% for the COF and wear rate. The regression coefficient \(p\)-value (\(<\)0.0001) indicates that the predicted model is significant. It was found that the \(p\)-value for factor C (water) was the most significant factor for both COF and wear rate with a percentage contribution of 67.21% and 54.42%, respectively. The \(R\)sq and adjusted \(R\)sq values were 0.9805 and 0.9707, respectively, for the COF which indicates that the regression model is significant, which shows an agreement between the experiments and prediction data. For wear rate, the \(R\)sq and adj-\(R\)sq values were 0.9564 and 0.9346, respectively. This also indicates the regression model is meaningful. Figure 3 shows the normal probability plot of COF and wear rate. The red dots are the experimental values and the blue lines are predicted values. It shows that the data are approximately normal distribution and the range of residuals rested approximately in a straight line. Hence, it could be noted that a quadratic model is adequate for anticipating the equations for both COF and wear rate. The prediction equations using RSM method for COF and wear rate were established by the quadratic statistical model as follow: \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Run Order**} & \multicolumn{2}{c}{**Actual Factor**} & \multicolumn{2}{c}{**Coefficient**} & \multicolumn{2}{c}{**Wear Rate**} \\ \cline{2-5}  & **A: Nanoparticles (wt \%)** & **B: SDS (wt \%)** & **C: Water (wt \%)** & **of Friction** & **(10\({}^{-10}\) cm\({}^{3}\)/N-m)** \\ \hline
19 & 0.75 & 1.5 & 20 & 0.0533 & 8.4527 \\
20 & 0.75 & 2 & 30 & 0.0571 & 9.2576 \\
21 & 1 & 0 & 50 & 0.0733 & 12.4779 \\
22 & 1 & 0.5 & 10 & 0.0523 & 9.0565 \\
23 & 1 & 1 & 20 & 0.0581 & 8.9559 \\
24 & 1 & 1.5 & 30 & 0.0628 & 9.6603 \\
25 & 1 & 2 & 40 & 0.0666 & 9.2578 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Source**} & **Degrees of** & **Sequential Sums** & **Adjusted Sums** & **Adjusted Mean of** & \multirow{2}{*}{_F-Value_} & \multirow{2}{*}{_p-Value_} & \% \\  & **Freedom** & **of Squares** & **of Squares** & **Squares** & & **Contribution** \\ \hline Model & 8 & 0.001570 & 0.001570 & 0.000196 & 100.55 & \(<\)0.0001 & 98.06 \\ A & 1 & 0.000292 & 0.000292 & 0.000292 & 149.52 & \(<\)0.0001 & 18.24 \\ B & 1 & 0.00064 & 0.00053 & 0.00053 & 27.27 & \(<\)0.0001 & 4.00 \\ C & 1 & 0.001076 & 0.000918 & 0.000918 & \(\mathcal{U}\)0.22 & \(<\)0.0001 & 67.21 \\ A\({}^{2}\) & 1 & 0.000134 & 0.000134 & 0.000134 & 68.51 & \(<\)0.0001 & 8.37 \\ B\({}^{2}\) & 1 & 0.00000 & 0.00000 & 0.00000 & 0.05 & 0.826 & 0.00 \\ C\({}^{2}\) & 1 & 0.000000 & 0.000000 & 0.000000 & 0.17 & 0.684 & 0.00 \\ \(\Lambda\times\) B & 1 & 0.000004 & 0.000003 & 0.000003 & 1.78 & 0.201 & 0.25 \\ A\(\times\) C & 1 & 0.00000 & 0.00000 & 0.00000 & 0.02 & 0.881 & 0.00 \\ Error & 16 & 0.000031 & 0.000031 & 0.00002 & - & - & - \\ \hline Total & 24 & 0.001601 & - & - & - & - & - \\ \hline \hline \end{tabular}
\end{table}