Generation of on-axis and off-axis conic surfaces of revolution by applying a tubular tool

A new technique, fabrication of aspherical ultraprecise surfaces using a tube, is applied to the generation of conic surfaces of revolution, which also demonstrates that it is possible to generate different kinds of surfaces with the same tube. Surfaces are considered that are generated with the same tube with an elliptical edge but with different off-axis distances and different angles between the tube and the surface. Subsequently it is shown that the generated surface is always a radial section of a conic surface. In addition it is proven that the shape of the generated conic surface is independent of the off-axis distance. With each elliptical tube edge a range of different conic surfaces can be made depending on the angle between tube and surface. The more the tube edge resembles a circle, the larger will be the range of different surfaces. For each tube an angle between the tube and the surface exists at which it generates an on- or off-axis part of a semi-ellipsoid. Finally, an optimization technique is presented for the determination of the best combination of process-determining parameters for the generation of a certain conic surface.