Hobbing mechanism of worm gear tooth surface with wave edges of double enveloping toroidal worm gearing

The double enveloping toroidal worm gear pair is a type of basic worm transmission with multi-tooth and double-line contacts. Tooth surfaces of the worm gear are hobbed by a toroidal worm gear hob which is produced based on the toroidal worm. The tooth surface of the hobbed worm gear is macroscopic non-smooth surface and have wave edges, and it is different with the theoretical worm gear tooth surface. In order to obtain the actual forming law of the hobbed worm gear tooth surface with wave edges, this article explores the hobbing principle based on hobbing processes. The actual hobbing mathematical model of the worm gear tooth surface are established, and the wave edges height is defined to evaluate the quality of the worm gear tooth surface. To preliminary obtain the characteristics of the hobbed worm gear tooth surface, the wave edges height distribution of left and right tooth surfaces are analyzed firstly. And then, the hob teeth of the hob are divided into different units to study the influence on the hobbed worm gear tooth surfaces, such as different spirals and different teeth. Further the influence of changing the total number of hob's chip grooves on the forming characteristics of worm gear tooth surfaces is studied. The results show that the wave edges on the left and right tooth surfaces of the toroidal worm gear are symmetrically distributed. And only some hob teeth have an effect on the final shape of the hobbed worm gear tooth surface, so these cutting teeth are key hob teeth of the toroidal worm gear hob. The total number of hob's grooves is mostly effect the wave height of the root circle position of the hobbed worm gear. The results provide important references for the design of a toroidal worm gear hob, which are helpful to obtain the high performance double enveloping toroidal worm gearing.