Study of the effective cutter radius for end milling of free-form surfaces using a torus milling cutter

•Importance of effective radius in studying milling of free-form surfaces with a torus cutter.•Establishing an analytical expression of the effective radius of a torus milling cutter working in translation.•Same expression used to calculate the effective radius near instantaneously.•Presentation of an industrial example showing potential use of the expression.

When end milling free-form surfaces using a torus milling cutter, the notion of cutter effective radius is often used to address the procedure for removal of material from a purely geometrical perspective. Using an original analytical approach, the present study establishes a relation enabling the value of this effective radius to be easily computed. The limits of validity of this relation are then discussed and precisely defined.By way of an illustration, an example of how this relation can be used to generate a numerical tool for analysis of the possibilities for machining free-form surfaces on multi-axis machine-tools is also presented.