# Operational Temperature Effect on Positioning Accuracy of a Single-Axial Moving Carrier
## 3 Results and Discussions
### Positioning Accuracies under Different Operational Temperature Conditions
At time = 160 min, the operational temperature reached a value of 31 \({}^{\circ}\)C. Afterward, the operational temperature gradually declined with time and gradually returned to the value of 23.5 \({}^{\circ}\)C at time = 338 min. However, in the case of winter nighttime hours, the initial operational temperature was approximately 23.7 \({}^{\circ}\)C which gradually decreased with time. At time = 249 min, the operational temperature was reduced to a value of 15.4 \({}^{\circ}\)C. Afterward, the operational temperature gradually rose with time. At time = 362 min, the operational temperature gradually returned to the value of 22.5 \({}^{\circ}\)C.  
Table 2 illustrates the corresponding positioning accuracies and corresponding variations of the moving carrier operating in summer daytime and winter nighttime hours. In the case of summer daytime conditions, the positioning accuracy slowly reduced with time as the operational temperature initially rose. However, as the operational temperature gradually declined to the value of 23.5 \({}^{\circ}\)C from 31.8 \({}^{\circ}\)C, the positioning accuracy significantly worsened from 11.33 to 15.74 \(\upmu\)m with a variation of 4.41 \(\upmu\)m and a variation rate of 0.00425 \(\upmu\)m/(min-\({}^{\circ}\)C). For summer daytime conditions, we found that a decline in the operational temperature (from 31.8 to 23.3 \({}^{\circ}\)C) caused the positioning accuracy to worsen for a periodically-moving carrier. In the case of winter nighttime conditions, while the operational temperature gradually declined from 23.7 to 15.4 \({}^{\circ}\)C, the positioning accuracy significantly worsened from 10.45 to 24.06 \(\upmu\)m with a considerable variation of 13.61 \(\upmu\)m and a variation rate of \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Time Point**} & \multirow{2}{*}{\begin{tabular}{c} **Chamber** \\ **Temperature** \\ **(\(\upmu\)C)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Time** \\ **(min)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Positioning** \\ **(\(\upmu\)m)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Variation of** \\ **Positioning** \\ **Accuracy** \\ **(\(\upmu\)m)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Variation Rate of** \\ **Positioning** \\ **(\(\upmu\)m/(min-\({}^{\circ}\)C))** \\ \end{tabular} } \\ \hline \multirow{2}{*}{1} & \multicolumn{2}{c}{Without temp.} & \multirow{2}{*}{22.7} & \multirow{2}{*}{0} & \multirow{2}{*}{18.30} & \multirow{2}{*}{0} & \multirow{2}{*}{0} \\  & control 0 & & & & & \\ \cline{2-6} \cline{1-1} \cline{3-6} \multirow{2}{*}{1} & \multicolumn{2}{c}{Without temp.} & \multirow{2}{*}{27.8} & \multirow{2}{*}{60} & \multirow{2}{*}{17.37} & \multirow{2}{*}{\(-0.93\)} & \multirow{2}{*}{\(-0.00304\)} \\  & control 60 & & & & & \\ \hline \multirow{2}{*}{2} & \multicolumn{2}{c}{Stable temp. 0} & \multirow{2}{*}{23.7} & \multirow{2}{*}{0} & \multirow{2}{*}{17.96} & \multirow{2}{*}{0} & \multirow{2}{*}{0} \\  & Stable temp. 100 & & & & & \\ \cline{2-6} \multirow{2}{*}{3} & Temp. rise 0 & & & & & \\ \cline{2-6}  & Temp. rise 63 & & & & & \\ \hline \multirow{2}{*}{4} & Temp. decline 0 & & & & & \\ \cline{2-6}  & Temp. decline 66 & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Corresponding positioning accuracy of the periodically-moving carrier under stable temperatures, a rise in temperature, and a decline in temperature. 0.00858 \(\upmu\)m/(min\(\cdot\)\(\mathrm{\SIUnitSymbolCelsius}\)). Afterward, as the operational temperature returned to 22.7 \(\mathrm{\SIUnitSymbolCelsius}\), the positioning accuracy still slowly worsened to a value of 26.61 \(\upmu\)m once more. In the two cases, we found that a decline in the operational temperature (from 23.7 to 15.4 \(\mathrm{\SIUnitSymbolCelsius}\)) causes the positioning accuracy to worsen greatly for a periodically-moving carrier in comparison to the effect of an operational temperature rise.