Contribution to the analytical determination of uncut chip thickness for cutting force modelling in milling with refinements for high-feed milling

Abstract

In modern manufacturing, accurately predicting cutting forces is essential for the design and control of machining operations. Common mechanistic models of cutting forces rely on a precise description of the local uncut chip area. However, in milling, the specific trajectories of cutting edges create challenges in modelling this quantity. Existing analytical models are typically limited to 2D contexts or assume circular tooth trajectories, which are mostly valid for cylindrical end mills. These assumptions limit their applicability to high-feed milling, especially due to low lead angles and complex insert cutter geometries producing non-circular paths. This article presents a new three-dimensional analytical model for evaluating the local uncut chip thickness in high-feed milling. It relies on closed-form expressions derived from geometric analysis and Taylor expansions to approximate the uncut chip area and cutter-workpiece engagement, even in regions where conventional models fail. The model applies to linear-path milling and accounts for tool run-out and differential pitch. Compared to a Newton-Raphson numerical method, it achieves a relative error below 5% while being 3 to 9 times faster, enabling efficient integration in force models. Beyond its computational efficiency, the explicit formulation enables analysis of geometric influence, such as sensitivity to feed per tooth or tooth count-capabilities not easily accessible with purely numerical approaches. This work contributes a rigorous and interpretable alternative for improving cutting force prediction in high-feed milling.