Stresses under the Tooth-Surface of Crowned Gears : Stress Problems on the Two Elliptic Bodies in contact with Each Other

Abstract

In the electric railcars whose motors are nose-suspended, the mis-alignment of gear-shafts inevitably happens in the power transmission mechanism, and if the end tooth bearing caused by the mis-alignment exists, gear-tooth surface failure will be induced. Therefore, in order to prevent the end tooth bearing, the nose-suspended type traction spur gears of the Japanese National Railways are heavily crowned. In these heavily crowned gears, tooth bearing is partial, but there is no end tooth bearing. Therefore, the bending stress calculation method for spur gears cannot be applied and the author introduced the calculation method for heavily crowned spur gears. These heavily crowned traction gears have higher rolling stresses than those of ordinary spur gears, but no tooth-surface failure has been reported on these crowned gears since this type of crowned gears was introduced as the nose-suspended type traction gears in 1956. Nevertheless, stresses under the tooth-surface must be clarified in connection with the tooth-surface strength and the depth of surface-hardening, but no satisfactory solution to these problems has been given until this day. The author treats this problem under five assumptions as follows : The tooth is replaced by a semi-infinite elastic body bounded by a plane which is loaded with a distributed perpendicular force and applying the theory on two elastic elliptic bodies in contact with each other, the author solves this problem with numerical calculations. Furthermore, the author examines the depth of surface-hardening and tooth-surface strength of heavily crowned traction gears of electric locomotives by calculating the stresses under the surface.