Estimating the radii of rounded cutting edges in milling tools using measured ploughing force

Accurately estimating the radius of the rounded cutting edge is crucial for studying the ploughing effect in milling, as it significantly influences the material flow mechanism, tool wear, and resulting surface quality. However, current methods fail to establish an analytical connection between this radius and process responses such as cutting force. To address this gap, this paper proposes a theoretical method for estimating the radius of the rounded cutting edge during milling. The method begins with the analytical derivation of an explicit relationship between the radius and ploughing force within the pure-plough cutting region. This is achieved through the development of a slip-line model that directly links shear stress to the rounded cutting edge and bridges the piling-up phenomenon with uncut chip thickness. Subsequently, the radius is determined by formulating an equation connecting the theoretical model with measured ploughing force in the pure-plough region. The required experimental ploughing force is extracted from measured cutting force data through mapping instantaneous uncut chip thickness to the minimum uncut chip thickness (MUCT). This thickness is theoretically determined by linking instantaneous cutting edge trajectories, influenced by tool runout, to tool deflections calculated based on measured cutting forces. Finally, a series of conventional and micro milling tests with various cutting parameters validate the effectiveness of the established method.