# Operational Temperature Effect on Positioning Accuracy of a Single-Axial Moving Carrier
## 2 Mathematical Theoretical Models and Experimental Methods  
### Structure of the Moving Carrier  
A periodically-moving carrier was used in this study, with an overall size of 1200 mm (length) \(\times\) 580 mm (width) \(\times\) 540 mm (height). The size of the moving carrier in the study was 500 mm (length) \(\times\) 500 mm (width) \(\times\) 110 mm (height), while the linear motor used in processing had a width of 195 mm and a height of 56 mm, as shown in Figure 1. A linear motor (GENTEC LC50100W2 AD&LS50216C, Shun-Peng Technology Co., Ltd, Taichung, Taiwan) was employed to drive the carrier, periodically moving along linear guideways.  
To maintain stable environmental temperature distribution in the processing area, an environmental control system was designed to supply the area with air at a constant temperature. The environmental chamber had a width of 1600 mm, a length of 2600 mm, and a height of 1100 mm. The size of the air inlet and outlet of the designed environmental system was 800 mm \(\times\) 150 mm. Figure 2 shows the relative position of the air inlets and outlets in the environmental chamber and the experimental setup in the study.  
Four thermocouple temperature detection components were laid outside the moving machine and near the heat source during the practical component processing to measure environmental temperature distribution in the process. Via this measurement, the heat power generated by the main heat sources could be estimated. In the study, the size of the environmental chamber is quite small and the flow field in the chamber is a laminar flow. The measured temperature deviations among the four thermocouples are less than 0.2 \({}^{\circ}\)C, and only the environmental temperature distributions around the moving carrier are our main concerns. Thus, four thermocouples were employed to measure the environmental temperatures around the moving carrier, as shown in Figure 2, and Figure 3 shows a schematic diagram of the environmental control system in the study. The temperature in the environmental chamber can be controlled by an air conditioning system. The returning air from the environmental chamber can be cooled down after passing through the evaporator, then the temperature of the process air can be compensated by a heater which is controlled by a PID controller in terms of the temperature measured by a thermocouple (PT100), as shown in Figure 3.  
Figure 1: Structural drawing of the moving carrier.  
Figure 2: The relative position of the air inlet and outlet in the environmental chamber during the numerical study and the experimental setup: (**a**) the air inlet and outlet are located on the same side of the chamber; (**b**) the air inlet and outlet are located on opposite sides of the walls; (**c**) image of the experimental setup; (**d**) Renishaw laser interferometer. The red circles in figures (**a**,**b**) represent the corresponding locations of the thermocouples in the experimental study.  
In order to control the temperature in the chamber, while the temperature measured by the thermocouple is less than the setting value, the process air is heated by the heater in terms of the feedback signals from the thermocouple.