Study on a method for rebuilding tooth surfaces of Planar Double-Enveloping Toroidal Worm-Gear

In order to manufacture planar double-enveloping toroidal worm-gear by CNC technology, an accurate 3-D digital model of each tooth must be constructed. This paper introduces a method for rebuilding analytical conjugating surfaces on each tooth of the worm-gear by Bernstein-Bezier interpolating method. Firstly, a family of cross sections, which has the same axis with the worm-gear, is hypothetically applied to intersect with theoretical meshing lines on a worm-gear tooth to generate a sequence of scattered data points. Then, based on all strictly defined boundaries on a tooth, Bernstein-Bezier triangle patches are utilized to interpolate all scattered data points to rebuild the tooth surfaces. During this interpolating processing, an algorithm for smoothing edges of every two adjacent patches is used for obtaining G1 smoothness on whole interpolating surfaces of a tooth. By this way, a 3-D digital model of the worm-gear is constructed and can be used for CNC manufacturing.