hp-finite element simulation of thermoelastic deformation in NC-milling

Andreas Schröder , Andreas Byfut , Raffael Joliet , Tobias Surmann

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

MSC 2000

74F05 Thermal effects

74S05 Finite element methods

PACS: 65.40.De

Abstract
This paper presents an $hp$-finite element approach for the simulation of heat diffusion and thermoelastic deformation in the NC milling process. Varying complex shapes resulting from the material removal are taken into account via a removal-dependent mesh refinement that relies on the isotropic bisection of hexahedrons intersecting the geometry of the milling tool in contact. To represent the cutting surface more accurately, the hexahedrons at the cutting surface are further subdivided into tetrahedrons, pyramids and prisms. To avoid the involved application of higher-order shape funtions on these shapes, and to enable the exclusive use of tensor product shape functions on hexahedrons, a fictitious domain approach is used. Numerical experiments show the applicability of the proposed method.