A fictitious domain method for the simulation of thermoelastic deformations in NC-milling processes

This paper presents a (higher-order) finite element approach for the simulation of heat diffusion and thermoelastic deformations in NC-milling processes. The inherent continuous material removal in the process of the simulation is taken into account via continuous removal-dependent refinements of a paraxial hexahedron base-mesh covering a given workpiece. These refinements rely on isotropic bisections of these hexahedrons along with subdivisions of the latter into tetrahedrons and pyramids in correspondence to a milling surface triangulation obtained from the application of the marching cubes algorithm. The resulting mesh is used for an element-wise defined characteristic function for the milling-dependent workpiece within that paraxial hexahedron base-mesh. Using this characteristic function, a (higher-order) fictitious domain method is used to compute the heat diffusion and thermoelastic deformations, where the corresponding ansatz spaces are defined for some hexahedron-based refinement of the base-mesh. Numerical experiments compared to real physical experiments exhibit the applicability of the proposed approach to predict deviations of the milled workpiece from its designed shape because of thermoelastic deformations in the process.