Abstract
Helical gears with localized bearing contact of tooth surfaces achieved by profile crowning of tooth surfaces are considered. Profile crowning is analyzed through the use of two imaginary rack-cutters with mismatched surfaces. The goal is to determine the dimensions and orientation of the instantaneous contact ellipse from the principle curvatures of the pinion and gear tooth surfaces. A simplified solution to this problem is proposed based on the approach developed for correlation of principal curvatures and directions of generating and generated tooth surfaces. The equations obtained are applied to three cases of profile crowning where the normal profiles of the rack-cutters are: (i) parabolic curves: (ii) circular arcs; and (iii) a combination of a straight line for one of the rack-cutters and a parabolic curve or a circular arc for the mating rack-cutter. The gear drives can be the combination of a pinion generated by a parabolic curve or a circular arc and gear generated by one of three cases mentioned above.
