Mathematical Model of Manufacturing a Novel Type of Hourglass Worm with Circular Tooth Profiles

A novel type of hourglass worm is considered, whose surface is formed by the locus of a circular blade. The worm has circular tooth profiles, which are relatively plain. According to the generation mechanism, the mathematical model for precisely manufacturing this kind of worm is developed, especially including the equation of the worm screw surface. A method to calculate the worm tooth profile is proposed. A numerical example is given to demonstrate the validity of the mathematical model and the proposed method.