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

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractThe 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.Keywords: Cutting force modelling, Edge discretisation, Tool geometry, Homogeneous matrix transformations, Turning operations Nomenclature α ne Working normal clearance angle; defined in P n [1] α P n Normal clearance angle given by the local preparation (P) of the insert; defined in P n α oe Working orthogonal clearance angle; defined inWorking normal rake angle; defined in P n [1] γ P n Normal rake angle given by the local preparation (P) of the insert; defined in P n ε E Tool included angle of the cutting edge (E); also denoted ε r if the cutting edge is included in P r [1] η Chip flow angle θ Polar angle defined in a coordinate system linked to the insert (parameterisation of the cutting edge) Θ Polar angle defined in a coordinate system linked to the machine (Θ = θ + κ r + ε r /2 − π/2) κ r Tool minor cutting edge angle; defined in

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