Meshing theory of involute worm drive.

• A novel meshing theory of the involute worm drive is built by geometry. • It is proved that the helical surface with constant helix parameter ground by plane is an involute helical surface. • The prove complements the principle for grinding the involute worm with the planar grinding wheel. • The meshing performance of the involute worm drive is studied in depth. • The calculation methods of meshing performance for involute worm drive are proposed. The subject of this paper is the establishment of a new meshing theory applicable to the involute worm drive. The method is proposed for determining the meshing characteristic parameters of the involute worm drive using the principal frame on the involute helicoid. A rigorous proof is presented to prove that a helicoid with constant helix parameter ground by a planar grinding wheel is an involute helicoid employing the uniqueness theorem for surfaces in differential geometry. The relationship among the helix angle of base circle, normal pressure angle and helix angle for the involute worm is proved. Using the proposed meshing theory, the numerical simulation of the involute worm drive is carried out to investigate the meshing performance of the involute worm drive. The numerical results reflect that the conjugate zone covers almost the entire worm gear tooth surface. The contact frequency is higher on one side of the worm gear tooth surface. The contact stress is higher near the end face of worm gear. An area of poor lubrication exists in the middle of the worm gear tooth surface. [ABSTRACT FROM AUTHOR]