The offset approach of machining free form surface: Part 2: Toroidal cutter in 5-axis NC machine tools

The offset approach of machining free form surface with cylindrical cutter is described in part 1 of this paper. This approach can also be used for other type of cutters, such as toroidal cutter, filleted end mill or drum cutter. From the point of view of the geometry, all these cutters can be called toroidal cutters. Based on this approach, the geometrical theory of machining free form surface by toroidal cutter in 5-axis NC machine tool is investigated in this paper. The process of enveloping machining free form surface has been converted into a line contact problem between the tracing surface of the circle and the offset surface of machined surface. The condition of the second order line contact and the third order osculating contact between the cutter surface and the machined surface is given. The orientation of the toroidal cutter and geometrical remained errors are calculated. By means of the proposed machining method, the machining precision and the efficiency can be improved, and the potential capacity of the 5-axis NC machine tools could be exploited. A numerical example is provided at the end of this paper for illustration.