## 4 Conclusions  
This study extends previous research by further developing the machine tool integrated inverse multilateration (MIM) methodology to assess the impact of ambient thermal variations on medium- and large-scale machine tools in industrial environments. By embedding an absolute distance measurement device within the spindle, the MIIM methodology provides an automated approach to volumetric error characterisation, eliminating reliance on controlled conditions, expensive thermal monitoring equipment, or dedicated calibra  
Figure 24: FEM simulation vs measured data. Second test, from 23 to 26 February. Position 2 (intermediate ram extension). \begin{table}
\begin{tabular}{c c c c} \hline  & **Travel Y (mm)** & **MAE [\(\upmu\)m]** & **RMSE [\(\upmu\)m]** \\ \hline Position 1 & \(-\)1350 & 13.1 & 16.3 \\ \hline Position 2 & \(-\)700 & 13.3 & 17.3 \\ \hline \end{tabular}
\end{table} 
Table 10: Comparison metrics between measured values and FEM model predictions. tion artefacts. This advancement makes the MIIM method a practical tool for evaluating thermal distortions in real-world manufacturing settings. The methodology has been applied to the assessment of large-scale machine tools operating under fluctuating thermal conditions, offering a reliable and scalable solution for automated error evaluation. Its adaptability to different machine configurations, control systems, and environmental conditions underscores its potential for broad industrial application. Comprehensive testing has demonstrated the robustness of the MIIM method, facilitating continuous, unattended data collection over extended periods. The results confirm its effectiveness in detecting thermally induced errors in large machine tools while addressing critical challenges in thermal error assessment, such as the need for low measurement uncertainty, full volumetric coverage, and the efficient monitoring of temperature-related deviations. Validation experiments were conducted on two distinct machine architectures--THERA(tm) (gantry type) and ZERO(tm) (bed type)--within standard workshop conditions, without altering the ambient environment. These trials complement earlier investigations involving the ARION(tm) (bridge type) machine, reinforcing the MIIM method's applicability across diverse machining platforms. Long-term testing revealed a strong correlation between thermal error patterns and ambient temperature fluctuations, validating the methodology's reliability for autonomous monitoring over extended durations. Further validation was achieved through a combination of first-order analytical models and finite element simulations, confirming ambient temperature variations as the primary driver of the observed thermal deviations. This integration of experimental data with simulation models strengthens the foundation for future refinements in machine tool performance optimisation and thermal compensation strategies. The principal outcomes of this research include:  
* Applicability to large MTs: The investigations using gantry- and bed-type machines, alongside prior work on bridge-type machines, demonstrate the methodology's applicability to large-scale MTs;
* Customisable parameters: Measurement points and traversal paths can be tailored to the experimental objectives, enabling rapid measurements during fast temperature changes or a higher resolution during gradual variations;
* Full automation: The system operates autonomously, enabling continuous measurement cycles without manual intervention and allowing hundreds of measurements to be conducted consecutively over multiple days;
* Controller compatibility: The system supports HEIDENHAIN and SIEMENS controllers, demonstrating versatility across different machine setups;
* Thermal dynamics insights: The MIIM method identifies critical parameters such as the frequency, amplitude, and temperature gradients of ambient air temperature changes, aligning with the ISO 230-3:2020 standards [29] and enhancing its industrial relevance.