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 provided by application of two imaginary rack-cutters with mismatched surfaces. The goal is to determine the dimensions and orientation of the instantaneous contact ellipse that requires the determination of principle curvatures of pinion-gear tooth surfaces. A simplified solution to this problem is proposed based on the approach development for correlation of principal curvatures and directions of generating and generated tooth surfaces. The obtained equations are applied for profile crowning where the normal profiles of the rack-cutters are either a circular arc or a straight line.