Cutting effectiveness in machining a spherical surface

Abstract

This paper provides an analytical solution to describe the trajectories of fixed cutting edges in machining spherical surfaces when the relative motion between the cutting edges and the workpiece surface involves three independent rotations. The concepts of surface coverage ratio and trajectory uniformity were introduced to measure the efficiency of machining the curved surfaces. The effects of the maximum half-swing angle, rotational speeds and rotational direction of the tool and workpiece on the uniformity of the trajectory pattern were analysed in detail. It was found that with the aid of the analytical solution, an optimal machining condition can be obtained, which enables a uniform distribution of the cutting edge trajectories and a good surface coverage in a short period of machining time.