Modeling swept envelopes of rotary cutting tools with application to five-axis flank milling

By representing the surface of revolution as a canal surface, an approach is presented to explicitly compute the swept envelope of a general rotary cutter and its first and second fundamental forms. Following the ANSI and ISO standards, two indices are defined to measure the normal deviation between the cutter envelope surface and the design surface, and their first order differential increments with respect to the differential deformations of both the tool surface and the tool axis trajectory surface are derived. These results provide a theoretical framework for design of the tool envelope surface that best matches the workpiece surface, and find many applications in the geometric problems rising from five-axis flank milling. Two examples of cutter location optimization are given to confirm the validity of the proposed methodology.