Abstract
This paper simulates the surface geometric error of line generated helicoids machined by rotating tools. The characteristic lines of rotating tool profiles are obtained based on theory of conjugate axes. The rotating tool profiles are developed by revolving the characteristic line about the tool axis. Mathematical models of the simulated helicoids are derived based on theory of conjugate surface, coordinate transformation, and differential geometry. Furthermore, the surface geometric error between theoretical and simulated helicoids is studied. Trapezoidal helicoid and Archimedean helicoid with variable pitches are chosen as the examples for the illustration of this approach.
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