The offset approach of machining free form surface: Part 1: Cylindrical cutter in five-axis NC machine tools

Based on the offset approach in differential geometry, the geometrical theory of machining free form surface by cylindrical cutter in five-axis NC machine tools is investigated in this paper. The process of enveloping machining free form surface has been converted into the second order line contact problem between the tracing surface of the tool-axis and the offset surface of machined surface. The condition of the second order line contact between the cutter surface and the machined surface is analyzed, and the calculating method of the cutter location is given. By means of the proposed machining method, the cusp height can be limited within the third order infinitesimal. The machining precision and efficiency can be improved, and the potential capacity of the five-axis NC machine tools can be exploited. Finally, several machining examples are given.