Determination of principal curvatures and contact ellipse for profile crowned helical gears

Helical gears with localized bearing contact of tooth surfaces achieved by profile crowning of tooth surfaces are considered. Profile crowning is prov ided by application of two imaginary rack-cutters with mismatched surfaces. The goal is to determine the dimensions and orientation of the instantaneo us contact ellipse that requires the determination of principle curvatures of pinion-gear tooth surfaces. A simplified solution to this problem is pro posed based on the approach developed in [1, 2] for correlation of principa l curvatures and directions of generating and generated tooth surfaces. The obtained equations are applied for profile crowning where the normal pr ofiles of the rack-cutters are either a circular are or a straight line.