# Operational Temperature Effect on Positioning Accuracy of a Single-Axial Moving Carrier
## 3 Results and Discussions
### Theoretical Models and Numerical Results of Flow and Temperature Fields
When the air inlet and outlet were designed on the same side of the chamber (cases C and D), the average temperature distributions above the moving carrier could be controlled at about 23 \({}^{\circ}\)C with a maximum variation of 0.4 \({}^{\circ}\)C. However, in cases A and B, in which the air inlets and outlets were located on opposite sides of the walls, it was found that the average temperature distributions along the moving path of the carrier were maintained within a deviation of 0.1 \({}^{\circ}\)C. In comparison to cases C and D, the flow fields in cases A and B exhibited a smooth and parallel flow pattern. Thus, the temperature deviations in those two cases were much less than those in cases C and D. Figure 8 shows the flow fields and temperature contours in the chamber in the cases where the air inlets and outlets were located, respectively, on opposite sides and on the same side at the inlet air velocity of 2.36 m/s. The flow field in the case where the air inlets and outlets were located on opposite sides exhibited a smooth and parallel flow pattern, and the heat can be effectively dissipated by flow convection in this case. Conversely, a large flow circulation was formed in the chamber in the case where the air inlets and outlets were located at the same wall, which may hinder the heat to dissipate from the air outlet, as shown in the figure. Thus, the temperature distributions on the linear guideway are higher than the case where the air inlets and outlets were located on opposite sides. Figure 7: Numerical average temperature distributions along the moving path of a periodic moving carrier. In addition, in this study, under the same feeding speed for a moving carrier, the positioning precision of the moving carrier varied with respect to the ambient temperature. From the dimensions of a single axial moving carrier, as shown in Figure 1, and the thermal expansion coefficients of the cast iron and stainless steel materials, as shown in Table 4, the positioning precision variation at 23.8 \({}^{\circ}\)C was estimated to be 22.8 \(\upmu\)m. In comparison to the experimental positioning precision variation at 23.8 \({}^{\circ}\)C, as shown at stable temp. 100 in Table 1, the estimated value is approximately 6.6 \(\upmu\)m larger than the experimental value. This is because the estimated value is calculated under a thermal steady-state condition. In the experiment, although the temperature was maintained for 100 min, the structural temperature of the moving carrier was still in a transitional state instead of a steady state. From the viewpoint of thermal diffusivity, the thermal diffusivity of cast iron is less than that of stainless steel, and the heat conduction speed in cast iron will be slower in the structure of a moving carrier. Thus, more time is required for the machine to reach a thermal steady-state condition in the experiment. In the cases in which the air inlet and outlet are located on opposite sides of the walls, the deviation distributions of the average temperature along the moving path of the carrier can be maintained in 0.1 \({}^{\circ}\)C due to parallel and stratified flow distributions. The positioning accuracy of 14.21 \(\upmu\)m for the carrier was experimentally measured in this case. The positioning accuracy's experimental value is less than the positioning accuracy's measured value of 16.14 \(\upmu\)m, as shown for the stable temp. 100 in Table 1, in the case in which the air inlet and outlet are located on the same side of the chamber. Thus, the air inlet and outlet locations on opposite sides of the walls are recommended in this study.