The worm conjugated with an ordered curl of involute cylindrical surfaces

Abstract

The involute teeth of straight or helical teethed wheels are usually machined with hob mill. The hob mills admit as primary peripheral surface a cylindrical helical surface with constant pitch. In this paper, based on the complementary theorem of “generating trajectories family”, it is demonstrated that the worm conjugated with an ordered curl of involute flanks is also an involute worm. The proposed development is based on analytical representations of the enwrapping surfaces with single point contact. In problem solving was applied the
method of intermediary surface (generating rack gear), developing the issue as a succession of enwrapping surfaces with linear contact. As application, it is presented a solution of the same issue in a graphical design environment — CATIA