# Operational Temperature Effect on Positioning Accuracy of a Single-Axial Moving Carrier
## 1 Introduction  
Demands for high production in the manufacturing industry are increasing due to global competition. The use of machine tools in current industrial development is required to generate higher productivity because of the great demand for products. Production speed, accuracy, and precision are also highly necessary as a form of product quality. The reliability of machine tools is one of the more important aspects that researchers have investigated [1; 2; 3; 4; 5]; however, the correlation between their reliability and environmental temperature has not been studied in depth. Whether it is the machine tools themselves or the outside environment, it is possible to impose direct or indirect impacts on processing accuracy. There is one problem in particular, namely, thermal deformation during processing, which has been receiving increasing attention in recent years [6; 7; 8]. In the past, most literature has engaged in investigations on thermal compensation to reduce thermal deformation from heat sources in machines. For a high rotating speed spindle (20,000 rpm), the largest thermal deformation can attain 180 \(\upmu\)m. It was found that the displacement-based thermal error model has much better accuracy and robustness than the temperature-based model [9]. [PERSON] et al. [10] described the effects on machine slide-guide contact conditions caused by thermal deformation. The thermal deformation of the table and the guide generated not only a change of motion that was straighter, but also pitching and yawing motion changes. The thermal distortion of the slide table caused a decrease in friction force of over 30% due to the non-uniformity of the slide contact between the table and the guide surface. [PERSON] et al. [11] investigated the influence of the runtime on positioning accuracy and thermal deformation of a high-speed feed system experimental bench. The thermal deformation caused by a rise in temperature is much greater than the geometric error of the feed system itself. As the runtimes of a feed system increase, the axial thermal deformations become larger, but after running for a period of time, the feed system approaches a thermal balance and reaches the approximate steady state, and the variations in thermal deformation ease up. In the literature [9; 10; 11], thermal deformations caused by frictional heat, heat of bearing contact, cutting force, and feeding speed have been investigated. The impact of environmental temperature variations on the positioning accuracy of machines was not considered. [PERSON] et al. [12] presented a novel offline thermal error modeling methodology using finite element analysis (FEA), which significantly determined the minimum experimental testing time required for a machine. A sample of the data shows that the FEA-based method correlated well with the experimental results, resulting in residual errors of less than 12 \(\upmu\)m. [PERSON] et al. [13] united two models to create a synthetic thermal error prediction model called the environmental temperature consideration prediction (ETCP) model. The proposed model shows high robustness and universality, with a thermal error over 85% and precision predicted by up to 0.2 mm. As the main equipment for advanced manufacturing technology, machine tools have been applied widely in many industries and regions. The types of machining workpieces also vary dramatically from user to user. Atmospheric pressure and temperature differ substantially from one region to another, and, therefore, machine tools are usually employed under many different working conditions [14]. During the processing of a machine tool, the environmental temperature of the processing area greatly influences the accuracy of the products. This raises the concern of effectively controlling the environmental temperature in the processing area while isolating pollution and interference from the outside environment. [PERSON] et al. [15; 16] studied thermal deformation inside the machine with the variation in environmental temperature.