Abstract: The forming theory of the tubular meshing tooth surfaces of conjugate-curve gears is established. An equidistance-envelope method is proposed based on the principle of conjugate curves. The meshing tube is generated by a sphere with an appropriate radius following a given equidistance curve of a given curve; the equations of equidistant curves and meshing tubes of conjugate curves are derived; and the tubular profiles are designed as parts of tubes inheriting all contact characteristics of conjugate curves. Three different contact patterns of tubular tooth profiles, convex-to-convex, convex-to-plane and convex-to-concave, are generated due to the different equidistance and directions. And the convex-to-concave tubular tooth profile has the smallest contact stress at the contact point due to the largest value of the relative curvature radius. An illustration of a cylindrical helix is presented; the equations of equidistance curves and meshing tubs of the conjugate curves are solved; and the models of conjugate-curve gears are set up.

Key words: conjugate-curve gears;meshing tube;tubular tooth profile;convex-to-concave;cylindrical helix