Basic Theory on Tooth Contact and Dynamic Loads of Gears. 3rd Report. A Pair of Tooth Profiles without Variation of Bearing Loads under Given Ratio of Angular Velocities.

Abstract

When the location of gear axes and the constant ratio of angular velocities are given, a pair of tooth profiles having a straight path of contact that coincides with the common contact normal at each point of contact is expressed by algebraic equations. The common perpendicular to the gear axes and the axis of relative rotation which is defined in the static space by the given ratio of angular velocities determine the static coordinate system, in which the design point P0 and the path of contact are determined as follows. In the case of cylindrical or bevel gears, P0 is chosen arbitrarily on the axis of relative rotation and the path of contact is chosen as a straight line through P0. In the case of other kinds of gears, P0 is chosen arbitrarily on the horizontal plane which includes the axis of relative rotation and is perpendicular to the common perpendicular, and the path of contact is chosen as a straight line through P0 which lies on the normal plane that is perpendicular to the relative velocity at P0. When the path of contact and its common contact normals are transformed to the coordinate systems rotating with each gear, a pair of tooth profiles without variation of bearing loads is obtained.