Free-form surface gear

摘要

A transmission gear has a tooth surface formed of a free-form surface instead of an involute surface and a root area formed of a free-form surface instead of a trochoid surface. With such a transmission gear, the fatigue strength against contact pressure can be increased by reducing the Hertzian stress in the area around the meshing point of the tooth surface. The tooth surface is formed of a free-form surface in which the smallest radius of curvature in an area around a mating pitch point is maximized, and the fatigue strength against bending can be increased by reducing the bending stress at a tooth root portion of the bottom land. In addition, the gear noise can be reduced. The bottom land is formed of a free-form surface in which the smallest radius of curvature in an area around a tooth root is maximized.

主权项

1. A transmission gear having a tooth surface and a tooth bottom land, said transmission gear comprising:
the tooth surface and the tooth bottom land having different free form surfaces; the free form surface of the tooth surface is formed of a first curved surface having a plurality of a radius of curvatures; the free form surface of the tooth bottom land is formed of a second curved surface having a radius of curvature; the first curved surface of the tooth surface has an area around a mating pitch point, wherein the smallest radius of curvature among a plurality of radii of curvatures in the area around the mating pitch point is maximized; the second curved surface of the tooth bottom land has a tooth root connecting to the tooth surface, wherein the radius of curvature around the tooth root is maximized; and wherein the first curved surface is formed of a compound surface of three different types of surfaces selected from one of the sets of: (a) a group of a cycloid helicoid surface, a trochoid helicoid surface, a circular helicoid surface, a limacon helicoid surface, a three-dimensional coordinate surface, an epitrochoid helicoid surface, a petritrochoid helicoid surface, and an involute helicoid surface; and (b) a group of a cycloid surface, a trochoid surface, an epitrochoid surface, a peritrochoid surface, a circular surface, a limacon surface, and an involute surface; and wherein the second curved surface is formed of a circular surface.