A generalised geometrical model of turning operations for cutting force modelling using edge discretisation

The knowledge of cutting forces is of prime importance to ensure the success of cutting operations, the desired properties of the machined parts and therefore the functionality of the workpieces. Edge discretisation is one way to model cutting forces. Traditionally used in milling, this methodology enables local changes in uncut chip thickness or cutting geometry to be taken into account and then gives suitable results in the three directions. A key point of this method is the geometrical transformation that enables the description of various tool geometries. This study proposes a geometrical model based on homogeneous matrices, whose main interest is to decompose the transformations step-by-step. The method, generalisable to all machining operations, is detailed for turning operations. Inserted cutters are modelled considering both the positioning of the insert and the local geometry of the insert. The cutting geometry and the edge are described using the same model in the machine coordinates system, allowing forces and moments to be calculated easily.