Gear

A gear having an involute tooth surface, wherein

• a tooth right-angled cross-sectional shape in a tooth bottom side area of a tooth is line symmetry with respect to a line connecting a tooth bottom center and a gear center;
• a half of the tooth right-angled cross-sectional shape in the tooth bottom side area of the tooth divided at the tooth bottom center as a boundary is defined by a first involute portion extending from the tooth bottom center toward the tooth surface, an arcuate portion connected smoothly to an end portion of the first involute portion, a second involute portion connected smoothly to an end portion of the arcuate portion, a third involute portion connected smoothly to an end portion of the second involute portion, and a tooth surface connecting curved portion connecting an end portion of the third involute portion and the tooth surface smoothly;
• the first involute portion is formed so as to be increased in radius of curvature with distance from the tooth bottom center;
• the arcuate portion is formed into an arcuate shape so as to have the same radius of curvature as the maximum radius of curvature of the first involute portion;
• the second involute portion is formed so as to have the same radius of curvature of a connecting portion with respect to the arcuate portion as the radius of curvature of the arcuate portion, and to be increased in the radius of curvature with distance from the arcuate portion;
• the third involute portion is formed so as to have the same radius of curvature of a connecting portion with respect to the second involute portion as the maximum radius of curvature of the second involute portion, and to be decreased in radius of curvature with distance from the second involute portion;
• the tooth surface connecting curved portion is formed of a smooth curved line which does not cause a stress concentration in a connecting area between the third involute portion and the tooth surface;
• a connecting portion between the second involute portion and the third involute portion is set to be positioned in the vicinity of a dangerous section position in a Hofer's 30 degrees tangent method;
• and
• the radii of curvature of the first involute portion, the arcuate portion, the second involute portion and the third involute portion are determined so that a stress variation width in a stress state of a so-called partly reverse state caused by a tensile stress and a compression stress generated in the tooth bottom side area of the tooth before and after the meshing of the tooth can be uniformized.