# Grain Size in Aluminum Alloy 6061 under Hot Ring Compression Test and after T6 Temper
## 3 Results  
### Friction Coefficient  
In this study, the influence of working temperature, upsetting speed, compression amount, and lubricant on the grain size were studied by using ring compression test. However, the friction coefficient for each experiment setup can be determined by computing the ratio of diameter to thickness of the specimen [5] as shown in Table 3.  
Although the friction coefficients shown in Table 3 are almost the same, if they are regarded as quality characteristics \(y\) as per Taguchi method, they possess the smaller-the-better property, which indicates the idea that the lower the friction coefficient, the more uniform the deformation. By means of signal-to-noise (S/N) ratio, which is also shown in Table 3 and defined as  
\[\text{S/N}=-10\log\frac{1}{n}\sum_{i=1}^{n}y_{i}^{2}, \tag{1}\]  
it can be observed that they are a little bit different. Based on Taguchi method, if the S/N ratios shown in Table 3 are averaged for each level of each factor, a response table can be obtained (Table 4) that describes the influence of each level of each factor on the quality characteristics. The greater the effect or the difference of S/N ratios between the levels of the same factor, the greater the influence of that factor on the quality characteristics. From Table 4, it can be observed that the effect of lubricant on the friction coefficient is the most significant (3.2 dB), followed by the working temperature (1.0 dB). The weakest effect is the upsetting speed (0.1 dB). Although the response table described above can exhibit how qualitatively significant the influence of the factor is on the quality characteristics, it is still not easy to quantitatively determine their influence strength. A statistical analysis of variance (ANOVA) is therefore needed. From Table 4, the mean value of the S/N ratio for each factor can be calculated at the same time. The sum of squares (SS) of deviations of each level from the mean of the factor can then be obtained as the variance for the factor. If the sum of squares is divided by degree of freedom (DF), which is the number of levels minus 1, the mean square (MS) or variance for the factor can be determined. The contribution (% C) of each factor to the quality characteristics was calculated by means of ANOVA, and the importance of each factor was also determined, as shown in Table 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Level No.**} & \multicolumn{4}{c}{**Factor**} \\ \cline{2-5}  & **Temperature** & **Speed** & **Compression** & **Lubricant** \\ \hline
1 & 13.8 & 13.3 & 13.4 & 11.6 \\
2 & 12.8 & 13.4 & 13.1 & 13.7 \\
3 & 13.4 & 13.3 & 13.6 & 14.8 \\ \hline effect & 1.0 & 0.1 & 0.5 & 3.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Response table of factors and their levels on friction coefficient based on signal-to-noise (S/N) ratio (unit dB) determined by Taguchi method. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Experiment No.** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline friction coefficient & 0.25 & 0.20 & 0.17 & 0.20 & 0.27 & 0.22 & 0.20 & 0.18 & 0.27 \\ S/N (dB) & 12.0 & 14.0 & 15.4 & 14.0 & 11.4 & 13.2 & 14.0 & 14.9 & 11.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Friction coefficient for each experiment setup determined according to [5] and its S/N ratio determined by Taguchi method. Since the factors with low variance could be considered random background noise, their SS and MS could then be pooled to error. Speed and compression have been determined to be part of the random background noise, as their contributions are as low as 0.11% and 1.92%, respectively. The resulting error calculation is as shown in the extra row with brackets in Table 5. Based on this pooling, it can be further noted that the contribution % C\({}^{\prime}\) of the lubricant is 92.46% and the working temperature has only 7.54% of contribution, approximately 12:1, which is not 3:1 as described in the response table.