It is quite difficult to manufacturing optical components, the combination of high gradient ellipsoid and hyperboloid,
with high machining surface requirements. To solve the problem, in this paper we present a turning and forming method
via oscillating feed of R-θ layout lathe, analyze machining ellipsoid segment and hyperboloid segment separately through
oscillating feed. Also calculate parameters on each trajectory during processing respectively and obtain displacement,
velocity, acceleration and other parameters. The simulation result shows that this rotary turning method is capable of
ensuring that the cutter is on the equidistance line of meridian cross section curve of work piece during processing high
gradient aspheric surface, which helps getting high quality surface. Also the method provides a new approach and a
theory basis for manufacturing high quality aspheric surface and extending function of the available twin-spindle lathe as
well.
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