# Operational Temperature Effect on Positioning Accuracy of a Single-Axial Moving Carrier
## 3 Results and Discussions
### Positioning Accuracies under Different Operational Temperature Conditions
control 60), the operational temperature rose to 27.8 \({}^{\circ}\)C, and the corresponding positioning accuracy was improved to 17.37 \(\upmu\)m. Thus, during the period of 60 min (\(t\) = 0 min to \(t\) = 60 min), the positioning accuracy variation was \(-\)0.93 \(\upmu\)m, and the positioning accuracy variation rate, in terms of time and operational temperature difference, was \(-\)0.00304 \(\upmu\)m/(min-\({}^{\circ}\)C). Compared to the case in which the operational temperature was controlled at a value of 23 \({}^{\circ}\)C with a 0.5 \({}^{\circ}\)C variation, the positioning accuracy improved from 17.96 to 16.14 \(\upmu\)m, the positioning accuracy variation was \(-\)1.82 \(\upmu\)m, and the positioning accuracy variation rate was \(-\)0.0182 \(\upmu\)m/(min-\({}^{\circ}\)C) over a period of 100 min from stable temp. 0 to stable temp. 100. In the case with a stable operational temperature, the positioning accuracy attained an improvement of 2.16 \(\upmu\)m (18.3-16.14 \(\upmu\)m) in comparison to the prior case. For the case with a stable operational temperature, the accuracy variation and accuracy variation rate were greatly improved over those in the case without a temperature control. This implies that, in the case with a stable operational temperature, the positioning accuracy gradually improved with time and temperature variation. Table 1 also indicates the corresponding positioning accuracy of the periodically-moving carrier under operational conditions for both temperature rise and decline. The table shows that in the case with an operational temperature rise, the initial operational temperature was 23.8 \({}^{\circ}\)C and the corresponding positioning accuracy was 16.14 \(\upmu\)m. The operational temperature then gradually increased to attain a value of 33.3 \({}^{\circ}\)C at \(t\) = 63 min, at which time the corresponding positioning accuracy reached 20.69 \(\upmu\)m. During the period of 63 min (\(t\) = 0 min to \(t\) = 63 min) when the temperature rose, the positioning accuracy variation was 4.55 \(\upmu\)m and the positioning accuracy variation rate  
Figure 5: Temperature distributions within the environmental chamber with stable environment, temperature raise, and temperature decline modes. was 0.0076 \(\upmu\)m/(min-\({}^{\circ}\)C). This phenomenon indicates that with a rise in operational temperature, the positioning accuracy worsens with time and an increase in operational temperature. As indicated in the table, the initial operational temperature was 23.6 \({}^{\circ}\)C, and the corresponding positioning accuracy was 14.93 \(\upmu\)m. In the case of an operational temperature decline, the operational temperature gradually declined to attain a value of 15.7 \({}^{\circ}\)C at \(t\) = 66 min at which time the corresponding positioning accuracy reached 22.94 \(\upmu\)m. During the temperature decline period of 66 min (\(t\) = 0 min to \(t\) = 66 min), the positioning accuracy variation was 8.01 \(\upmu\)m, and the positioning accuracy variation rate was 0.01536 \(\upmu\)m/(min-\({}^{\circ}\)C). From the positioning accuracy variations in the case of an operational temperature decline, it is found that, for the periodically-moving carrier, positioning accuracy can substantially worsen with time and operational temperature decline. To investigate the variations in positioning accuracy for a periodically-moving machine in summertime and wintertime, an air conditioning system was designed to simulate the operational temperature distributions in the daytime in summer and in the nighttime in winter, respectively. Figure 6 illustrates the temperature distributions within the chamber in the daytime in summer and in the nighttime in winter, which were generated by the designed air conditioning system. In the case of summer daytime hours, the initial operational temperature was approximately 23.5 \({}^{\circ}\)C, which gradually rose with time.