## 3 Experimental Tests and Results
### THERA(tm) Machine Tests
#### 3.1.1 First Test: Low Ambient Temperature Variation  
The first test was conducted over three consecutive working days without interruptions and under stable ambient temperature conditions. This near quasi-stationary scenario was achieved due to the climate-controlled shop floor, which maintained stable temperatures during the day. Additionally, warm nights resulted in minimal overnight temperature drops, with variations of less than 1 \({}^{\circ}\)C. During this period, 86 complete MIMO measurements were performed. Figure 9 shows the geometric deviations at each of the 74 measured points (refer to Figure 2) across the 86 MIMO measurements conducted from 24 to 27 October 2023. The average ambient temperature during this period was approximately 20 \({}^{\circ}\)C, fluctuating between a minimum of 18.8 \({}^{\circ}\)C and a maximum of 20.5 \({}^{\circ}\)C (refer to Table 4), with very stable conditions during working hours. The superimposed data in the figure, forming a narrow \begin{table}
\begin{tabular}{c c c c c} \hline
**Test Days** & **Taverage (\({}^{\circ}\)C)** & **Tmax (\({}^{\circ}\)C)** & **Tmin (\({}^{\circ}\)C)** & **AT (\({}^{\circ}\)C)** \\ \hline
24–27 October & 19.99 & 20.50 & 18.79 & 1.71 \\
30 October–7 November & 19.21 & 20.85 & 16.87 & 4.02 \\ \hline \end{tabular}
\end{table} 
Table 4: Average, maximum, minimum, and absolute ambient temperature variations recorded on tests conducted during October–November 2023 on climatised shopfloor. Figure 8: Measured air temperature near the THERATM machine. band, highlight the minimal repeatability error of the MIM methodology compared to the absolute geometric error of the MT. Geometric deviations along the X, Y, and Z axes are denoted as Ex, Ey, and Ez, respectively. Table 5 provides the maximum and average standard deviation values for the X, Y, and Z axes that were calculated for this experiment, referring to Figure 9.  
The results indicate that the volumetric errors or deviation variations were small during this experiment. However, even under stable ambient conditions, the machine tool errors exhibited a delayed response to the temperature trends. Due to the symmetrical design of the machine, this effect was most prominent along the Z-axis, where the columns and ram expanded or contracted in proportion to ambient temperature changes (refer to Figure 6). Figure 10 illustrates the evolution of the environmental temperature variation error (ETVE) in the Z direction at a specific point within the measurement point cloud, corresponding to a Y-centred position and maximum ram extension (Point P_25 in Figure 2). A clear correlation is observed between temporal fluctuations in the point deviation and ambient temperature changes. As the temperature increases, the error grows in a positive direction, effectively making the machine appear larger, with a certain delay. Conversely, as the temperature decreases, the error shifts in a negative direction, making the machine appear smaller. The error remains stable in the absence of temperature fluctuations. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **X-Axis (\(\mu\)m)** & **Y-Axis (\(\mu\)m)** & **Z-Axis (\(\mu\)m)** \\ \hline Average & 5 & 8 & 12 \\ \hline Maximum & 10 & 12 & 17 \\ \hline \end{tabular}
\end{table} 
Table 5: Maximum and average standard deviation values for the MIM test performed from 24 to 27 October 2023 (results in \(\mu\)m). Figure 9: Measured geometric deviation for THERATMATESEX, Ey, and Ez (first test: low ambient temperature variation). 3.1.2. Second Test: Extended Duration and Greater Environment Variability  
The second significant test was conducted over eight uninterrupted days, during which the ambient temperature exhibited greater variations compared to the first test.