Deterministic modelling of end-milled sidewall topography with tool runout, tooth-radius difference and stationary cutter deflection

Abstract

End milling is widely used to manufacture ribs, pockets, frames, and other structural features in mechanical and aerospace components. The resulting sidewall topography can affect dimensional accuracy, functional performance, and fatigue behaviour, so its prediction is relevant during process planning. This study develops a deterministic three-dimensional model for a sidewall produced by a two-tooth end mill. The mathematical framework accounts separately for radial runout, tooth-radius difference, angle-dependent chip formation, transverse cutting forces, and stationary cutter deflection. The surface is first reconstructed from the helical trajectories of the cutting edges. The in-plane force relation is parameterised using an open FEM-derived dataset for AL6061; during each tooth passage, chip thickness and force vary with angular immersion, while the helix angle produces progressive engagement along the axial direction. After a repeatable force cycle is obtained, the transverse slice forces are averaged over that cycle, converted to a distributed load, and applied to a stationary Timoshenko beam model. The calculated beam displacements are then used in the subsequent reconstruction of the sidewall topography. Four staged scenarios are compared: ideal geometry, radial runout, runout with unequal tooth radii, and runout with unequal tooth radii and stationary cutter deflection. For the selected numerical case, runout caused one tooth to form most of the retained feed marks, whereas tooth-radius difference mainly changed wall position and transverse load. Under the adopted cycle-mean-load assumption, cutter deflection changed the axial form and wall position but did not create a new time-resolved local feed-mark pattern. The ideal numerical profile differed from the analytical translating-trochoid reference by less than 0.1%, and the predicted free-end displacement was 6.63 µm. The numerical results provide a basis for subsequent comparison with measured forces, cutter displacement, and surface topography. This manuscript is a preprint and has not undergone peer review. Author: Roman Oleksandr Serhiiovych.Author: Myhovych Artur Volodymyrovych.Corresponding author: Myhovych Artur Volodymyrovych, myhovych.artur@lll.kpi.ua. Affiliation: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” License: Creative Commons Attribution 4.0 International (CC BY 4.0).