Mathematical model and undercutting analysis of elliptical gears generated by rack cutters

The theory of gearing and geometry of the straight-sided rack cutter are employed to develop a mathematical model of elliptical gears that takes backlash into consideration. The mathematical model also includes the bottom land of the elliptical gear, which is equidistant from the pitch ellipse. A computer program is developed to generate the tooth profile of elliptical gears. The profile of elliptical gears obtained by applying the proposed method is compared with that obtained by the evolute method. Undercutting of elliptical gears is also investigated. The results of this research should be helpful in the design, manufacture, and measurement of elliptical gears. Copyright 1996 Elsevier Science Ltd