On the determination of fully conjugate hypoid tooth flanks

Presented is a procedure to individually specify fully conjugate hypoid gear tooth flanks. Cartesian coordinates for the hypoid tooth flanks are derived in terms of a planar rack with a specified constant pressure angle. These coordinates define a “coordinate curve” on the tooth flank. Each coordinate curve depends on an axial coordinate and the entire tooth flank is established as a family of these coordinate curves. This process results in global interference between locally conjugate hypoid tooth flanks if the pressure angle is constant. A differential equation is established for the axial variation in the rack's pressure angle to avoid global interference. The resulting axial variation in normal pressure angle is combined with the determination of coordinate curves to obtain fully conjugate tooth flanks. An automotive hypoid gear pair is presented to showcase the process. Unloaded Ease-off (UEO) topography is used to quantify conjugate action for the example hypoid gear pair. Subsequently, axial and transverse profile modifications are applied individually to the ideal tooth flanks to accommodate generalized loading conditions. Loaded Transmission Error (TE) and maximum contact pressure are reported for a set of input torques.