Flat-end cutter orientation on a quadric in five-axis machining

•The conditions to avoid local gouging and rear gouging are formulated.•The machined strip width is evaluated analytically.•Two orientation angles are fully exploited to maximise the width without gouging.•The theory has been successfully applied in 5-axis sculptured surface machining.

The authors have recently developed methods for cutter orientation and tool path generation in 5-axis sculptured surface machining, where the design surface is approximated locally by a quadric. This paper presents, from a purely geometric perspective, the fundamental theory for optimising the cutter orientation on a quadric, which maximises the machined strip width whilst avoiding local and rear gouging. The analysis focuses on the flat-end cutter which is modelled by a circular cylinder but can be generalised for any fillet-end cutter using an appropriate offset of the design surface and the concept of geometric equivalency. The theory is illustrated by three examples.