Numerical cutting simulation of globoidal worm gears meshing with arbitrary shaped gears

Abstract In this paper, a numerical cutting simulation for generating globoidal worm gear flanks meshing with arbitrarily shaped gears is presented. The method extends conventional cutting simulation techniques to accommodate the large helix angles and double rotation characteristic of globoidal worms. By defining tool surfaces parametrically—using tool types such as the hob gear, grinding wheel, and finger milling cutter—and applying a root-finding algorithm, the envelope curves in the axial cross section are accurately determined. These two-dimensional envelope curves are then transformed into a three-dimensional tool surface through coordinate transformations. The resulting globoidal worm flank is analyzed in a tooth contact analysis (TCA) with a cylindrical helical gear, where comparisons of different tool kinematics reveal that manufacturing with the hob gear yields superior flank conformity. In contrast, methods using a grinding wheel or finger milling cutter tend to produce undercutting, particularly at the edges of the gearing length, leading to reduced tooth contact areas. The simulation highlights the importance of controlling tooth gap variations and achieving high manufacturing accuracy to optimize load capacity and efficiency. Overall, this approach offers significant potential for enhancing worm gear technology through improved design and manufacturing strategies.