Thermo-elastic deformations represent one of the main reasons for positioning errors in machine tools. Investigations of the thermo-mechanical behaviour of machine tools, especially during the design phase, rely mainly on thermo-elastic simulations. These require the knowledge of heat sources and sinks and assumptions on the heat dissipation via convection, conduction and radiation. Forced convection such as that caused by moving assemblies has both a large influence on the heat dissipation to the surrounding air. The most accurate way of taking convection into account is via computational fluid dynamics (CFD) simulations. These simulations compute heat transfer coefficients for every finite element on the machine tool surface, which can then be used as boundary conditions for accurate thermo-mechanical simulations. Transient thermo-mechanical simulations with moving assemblies thus require a CFD simulation during each time step, which is very time-consuming. This paper presents an alternative by using characteristic diagrams to interpolate the CFD simulations. The new method uses precomputed thermal coefficients of a small number of load cases as support points to estimate the convection of all relevant load cases (i.e. ambient conditions). It will be explained and demonstrated on a machine tool column.

Thermal errors are one of the major contributors towards positioning discrepancies in machine tools in precision machining. Along with friction and waste heat generated from production processes and internal heat sources, environmental influences around the machine tool create considerable thermal gradients followed by non-linear structural deformations. Efficient quantification of these three contributing sources of thermal errors are required in order to formulate a reliable thermal-error compensation system. The creation of all possible thermal configurations, which a machine tool could be subjected to, is experimentally infeasible and requires complex and time-consuming coupled flow and thermo-structural simulations. This paper presents a new approach in thermal error prediction by using CFD and finite element (FE) simulations to train a three-level interconnected neural network system. The first level essentially decouples flow simulations from thermo-structural simulations using optimal FE node points found using a Genetic Algorithm (GA), which significantly reduces the required training data. The boundary convection data obtained from this level is used in the second level to predict possible thermal configurations of the machine tool, after careful consideration of parameters related to internal heat sources and production processes. The third level maps these thermal configurations onto displacements on the machine tool.