The Conditions of Undercut By Shaping Using a Rounded Profile Gear Shaper Cutter

Abstract

Abstract The present paper deals with the cases of undercut when not only the linear but the curved segment of the generatrix curve is also taken in consideration. The literature admits the approximation of the root fillet with a circular arc with a radius of 0,38 m. In this paper, instead of this approximation, the real envelope realized by the rounded rack-head is computed. In analyzing the undercut there are two classical synthetic geometrical models supporting Litvin’s general equations that describe the condition of avoiding the undercut: one for the linear and one for the rounded part of the generatrix. The scope of exact computing of the root fillet curve consists in optimizing the cutting toll tooth topland geometry to obtain the best rigidity. The numerically evaluated models allow us to conclude that profile shifting can be pushed below the undercut limits stated in the classical literature, without the appearance of the well-known fracture point on the meshed tooth profile.