Generalising the Machine Tool Integrated Inverse Multilateration Method for the Ambient Thermal Error Analysis of Large Machine Tools in Industrial Environments

This study expands on prior research by generalising the machine tool integrated inverse multilateration methodology to evaluate ambient thermal effects on medium- and large-sized machine tools in industrial environments. This method integrates an absolute distance measurement device into the machine tool spindle, enabling an automated and robust multilateration scheme without requiring controlled environments, expensive thermal instruments, or specialised artifacts. Tests were conducted using a LEICA AT960™ laser tracker and wide-angle retro-reflectors (both from Hexagon Manufacturing Intelligence, Stockholm, Sweden) across two machine architectures, THERA™ (gantry type) and ZERO™ (bed type), building on earlier work with the ARION G™ (bridge type), all of them MTs manufactured by Zayer (Vitoria, Spain). Sequential experiments in varying ambient conditions demonstrated the reliability of the machine tool integrated inverse multilateration approach over extended periods, showing strong correlations between the measured errors and temperature variations. The results were validated using a first-order mathematical model and finite element method simulations, confirming thermal error evolution as a function of ambient temperature changes. This method’s adaptability to diverse machine architectures and industrial conditions highlights its potential for characterising and mitigating thermal errors in large machine tools. This work underscores the method’s effectiveness and utility for advancing thermal error analysis in practical manufacturing settings.