## 3 Experimental Tests and Results
### ZERO(tm) Machine Tests  
Between 12 and 26 February 2024, a new test campaign was conducted on the ZERO(tm) Zayer machine on the Zayer manufacturing shop floor. This campaign aimed to extend the MIIM methodology to a Heidenhain TNC7 CNC control system and assess its applicability to a different MT architecture, specifically a bed-type machine located in a non-climatised environment. Unlike previous tests, this environment had only a heating system for operator comfort, resulting in significant temperature variations during the two-week experiment.  
Several experiments were conducted during this period, defining a measurement point cloud comprising 84 points. Each MIIM measurement required 46 min and 24 s to complete. Figure 13 shows the linear axis reference system and details of the laser tracker mounted on the tool holder during the measurement procedures. The measured volume and resolution for each measurement were as follows:  
* X: \(\div\) 2.650 \(\div\) \(-\)1.350 (1.300 mm) with a step size of 260 mm (table horizontal movement);
* Y: \(-\)1.300 \(\div\) \(-\)100 (1.200 mm) with a step size of 240 mm (ram horizontal movement);
* Z: \(-\)1.150 \(\div\) \(-\)50 (1.100 mm) with a step size of 100 mm (vertical movement along the column).  
\begin{table}
\begin{tabular}{c c c c} \hline  & **X-Axis (\(\mu\)m)** & **Y-Axis (\(\mu\)m)** & **Z-Axis (\(\mu\)m)** \\ \hline Average & 12 & 8 & 33 \\ \hline Maximum & 21 & 15 & 37 \\ \hline \end{tabular}
\end{table}
Table 6: Maximum and average standard deviation values for the MIIM test performed between 30 October and 7 November 2023 (results in \(\mu\)m).  
Figure 12: Air temperature and ETVE in Z direction from 30 October to 7 November.  
Figure 14 illustrates the point cloud and movement sequence used in this test campaign, conducted on the ZERO(tm) machine tool.  
Two significant experiments, each lasting over three days and involving more than 100 complete MIM measurements, are detailed in the following sections. These experiments confirm the methodology's value in studying thermal errors induced by ambient temperature variations within a machine tool's working volume. The first experiment was conducted over three working days with substantial temperature fluctuations, while the second, longer experiment spanned a similar duration but included a weekend.  
Figure 15 depicts the evolution of the air temperature during the test campaign, showing significant drops during the night, with reductions of nearly 8 \({}^{\circ}\)C on the coldest nights. Rapid temperature recovery occurred each morning when the heating system was activated a few hours before the start of the workday. The test campaign also included two weekends.  
Figure 14: Measured points’ spatial distribution and movement sequence for the ZEROTM.  
Figure 13: ZEROTM machine test details: (**a**) reference system and (**b**) detail of the laser tracker attached to the tool holder.  
Two theoretical approaches were undertaken to mathematically validate that the measured error evolution depicted in the above figures was caused by ambient temperature variations:  
* First-Order Model: A first-order model was calibrated using data from one of the tests to identify key parameters, including the thermal time constant and proportional gain. This model was then used to generate a simulated response based on the temperature data from the first test. A comparison of the simulated output with the actual measured errors demonstrated a strong correlation, confirming the model's accuracy.
* Finite Element Method Analysis: The second approach entailed utilising the machine's FEM model to perform a transient thermal analysis, using temperature variations as the input. The predicted deformations were compared with the measured errors, once again validating that the observed error evolution is attributable to ambient temperature fluctuations.