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

TL;DR

This paper introduces a novel implicit-explicit multi-rate time stepping method for real-time finite element simulation of thermal deformation in machine tools, enabling accurate and fast modeling of heat distribution and deformation during manufacturing.

Contribution

It presents a new higher-order multi-rate time stepping method based on spectral deferred corrections, implemented with the open-source DUNE library for real-time FEM simulations.

Findings

Real-time coupled temperature and deformation simulation achieved.

Method outperforms traditional approaches in computational efficiency.

Validated on a machine tool model with sliding rails.

Abstract

Finite element models without simplifying assumptions can accurately describe the spatial and temporal distribution of heat in machine tools as well as the resulting deformation. In principle, this allows to correct for displacements of the Tool Centre Point and enables high precision manufacturing. However, the computational cost of FEM models and restriction to generic algorithms in commercial tools like ANSYS prevents their operational use since simulations have to run faster than real-time. For the case where heat diffusion is slow compared to machine movement, we introduce a tailored implicit-explicit multi-rate time stepping method of higher order based on spectral deferred corrections. Using the open-source FEM library DUNE, we show that fully coupled simulations of the temperature field are possible in real-time for a machine consisting of a stock sliding up and down on rails attached to a stand.