Contour Quality Evaluation of the Toroidal Cutter

A toroidal cutter is an effective tool for use in the machining of freeform surfaces. Its contact point on the machined surface creates a second-order continuous curvature, thus the scallop height is decreasing if the cutter axis is inclined at a suitable angle against the machined surface. However, few studies address the evaluation of the contour quality produced by this kind of cutter. The geometry of a toroidal cutter includes a cylindrical shank, cutting body, and a toroidal surface. These components may deviate from the ideal geometry, resulting in contour errors. Therefore, it is very important to evaluate the radius of the cutting body and the toroidal surface based on the axis of the minimal circumscribed cylinder. This paper first presents a reliable model to determine the axis of the minimal circumscribed cylinder (MCC) of the cutter shank, from measured data. Then, based on the determined axis, the radius of the cutting body is calculated, and finally the minimal circumscribed toroidal surface (MCTS) of the revolving surface of the corner arc is investigated. An illustrative example is given to verify the validity of this modelling methodology. This work provides a basis for evaluating the actual contour quality for this kind of rotating cutter. The method illustrated here can also be used for error evaluation for other kinds of cutter with a single shank having multiple cutting edges.