A unified analytical cutting force model for variable helix end mills

The paper proposes a unified analytical cutting force model based on a predictive machining theory for variable helix end mill considering cutter runout. The variable helix end mill is divided into a set of differential oblique elements along the axial direction. The cutting process of oblique element is based on the non-equidistant shear zone model and the equivalent plane method. The cutting forces of oblique element are modeled by shearing force components due to shearing at the shear zone and edge force components due to rubbing in the tertiary zone. In the primary shear zone, a modified Johnson-Cook model is introduced to account for the material size effect affected by varying instantaneous uncut chip thickness (IUCT) during milling process. In the tertiary zone, edge radius and the partial effective rake angle are included in the analytical model in order to take into account the rubbing effect precisely. The total instantaneous cutting forces are obtained by summing up the cutting forces acting oblique elements on all flutes. The unified analytical cutting force model is verified by experimental data using four different types of end mills, and a good agreement of the predicted and measured cutting forces shows that the proposed model is valid for variable helix end mills.