Thermal effects compensation and associated uncertainty for large magnet assembly precision alignment

Big science and ambitious industrial projects continually push technical requirements forward beyond the grasp of conventional engineering techniques. An example of these are the extremely tight micrometric assembly and alignment tolerances required in the field of celestial telescopes, particle accelerators, and the aerospace industry. Achieving such extreme requirements for large assemblies is limited, largely by the capability of the metrology used, namely, its uncertainty in relation to the alignment tolerance required. The current work described here was done as part of Maria Curie European research project held at CERN, Geneva. This related to future accelerators requiring the spatial alignment of several thousand, metre-plus large assemblies to a common datum within a targeted combined standard uncertainty $(u_{c}^{tg}(y))$ of 12 μm. The current work has found several gaps in knowledge limiting such a capability. Among these was the lack of uncertainty statements for the thermal error compensation applied to correct for the assembly's dimensional instability, post metrology and during assembly and alignment. A novel methodology was developed by which a mixture of probabilistic modelling and high precision traceable reference measurements were used to quantify the uncertainty of the various thermal expansion models used namely: Empirical, Finite Element Method (FEM) models and FEM metamodels. Results have shown that the suggested methodology can accurately predict the uncertainty of the thermal deformation predictions made and thus compensations. The analysis of the results further showed how using this method a ‘digital twin’ of the engineering structure can be calibrated with known uncertainty of the thermal deformation behaviour predictions in the micrometric range. Namely, the Empirical, FEM and FEM metamodels combined standard uncertainties $(u_{c}(y))$ of prediction were validated to be of maximum: 8.7 μm, 11.28 μm and 12.24 μm for the studied magnet assemblies.