Topography prediction in 5 axis milling of free form surfaces based on a realistic cutter edge and a new efficient algorithm

Predicting machined surface micro-topography in 5-axis milling of freeform surfaces remains difficult because the generated texture is governed by the combined effects of tool motion, local surface curvature, and the actual condition of the cutting edge. Existing N-buffer, swept-envelope, and Z-Map-based approaches commonly require a compromise between geometric fidelity and computational cost, particularly when realistic cutter-edge microgeometry must be represented over large micrometric-resolution surface areas. This work introduces the u and v rasterization map (UVRMAP), a simulation framework that couples automated cutter-edge extraction from high-resolution 3D measurements with a vectorized projection algorithm formulated in the intrinsic parametric domain of the nominal surface. Ideal, modeled, and experimentally reconstructed cutter edges can be incorporated, including edge-hone variations, wear flats, micro-defects, and stochastic irregularities. During simulation, the discretized cutting edge is rotated along the interpolated 5-axis tool path and projected onto the surface coordinates, allowing efficient computation of the resulting topography while preserving tooth-level geometric detail. The framework was experimentally validated on machined freeform surfaces by comparing measured topographies with simulations generated using ideal, modeled, and real extracted cutter edges. The results show that realistic cutter-edge descriptions improve the reproduction of fine surface marks and wear-induced height variations. UVRMAP also enables micrometric simulation over large freeform areas with around two orders of magnitude acceleration compared with classical Z-Map implementations. The proposed framework therefore provides an efficient and experimentally validated link between cutter-edge condition, 5-axis tool motion, and surface topography generation in precision finishing operations.