The region division and NC machining of compound surfaces

Compound surfaces are divided into three kinds of regions by the theory of differential geometry. The correlative mathematical models for defining the cutter parameters, the step-forward length, and the path intervals in the NC machining of the surfaces are described based on the feature of the regions. In the NC machining of the hyperbolic and parabolic region, the authors propose that the step-forward moves along the asymptotic direction and should turn a small angle towards the convex region so as to avoid interference. The prolonged step-forward length would result in improvement in machining efficiency.