Computerised simulation of meshing and contact of double enveloping worm gears

As a prerequisite for stress analysis of any gearing using Element Method (FEM), the most important stage in the analysis is the phase of pre-processing which involves the development of geometry and its meshing in order to determine the loading points. A new direct method is presented in this article for the determination of geometry of any gear surface based on the property of conjugate surfaces and differential geometry. The present study includes the geometric modelling of a double enveloping worm and its mating gear, the computerized simulation of meshing as well as the contact of the worm and gear. The double enveloping worm is cut by a straight-lined blade and the mating gear is cut by a hob that is identical to the geometry of the double enveloping worm. The envelope of the locus of cutter surfaces is determined using the direct method and is compared with the kinematic approach1. A computer coding has been developed to simulate the contact of the worm and gear at any instant.