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Finite element models without simplifying assumptions can accurately describethe spatial and temporal distribution of heat in machine tools as well as theresulting deformation. In principle, this allows to correct for displacementsof the Tool Centre Point and enables high precision manufacturing. However, thecomputational cost of FEM models and restriction to generic algorithms incommercial tools like ANSYS prevents their operational use since simulationshave to run faster than real-time. For the case where heat diffusion is slowcompared to machine movement, we introduce a tailored implicit-explicitmulti-rate time stepping method of higher order based on spectral deferredcorrections. Using the open-source FEM library DUNE, we show that fully coupledsimulations of the temperature field are possible in real-time for a machineconsisting of a stock sliding up and down on rails attached to a stand.

Toward transient finite element simulation of thermal deformation of machine tools in real-time