Mathematical model and worm wheel tooth working surfaces of the ZN-type hourglass worm gear set

In this study, the hourglass worm gear set is composed of a ZN-type hourglass worm generated by straight-edged blade cutters and a ZN-type hourglass worm wheel generated by worm-type hourglass hob cutters. Mathematical model of the ZN-type hourglass worm gear set is derived based on its generation mechanism and the theory of gearing. According to the developed mathematical model of the gear set, computer graphs of the ZN-type hourglass worm and worm wheel are presented. The tooth working surface, boundary lines and contact lines of the ZN-type hourglass worm gear set under different lead angles, pressure angles and modules are investigated and compared with those of the ZA-type hourglass worm gear set.