Efficient quantification of free and forced convection via the decoupling of thermo-mechanical and thermo-fluidic simulations of machine tools

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.