The Undercut Criterion of Pinion Shaper Cutters: And an Improvement by Modifying the Basic Rack Profile

The fillet of the gear tooth is highly stressed in operation; so for heavily loaded gears, the fillet geometry must be controlled. The manufacturer's task is to, within acceptable tolerances, produce the gear to the designer's specifications regardless of the manufacturing method. Most often gear cutting tools are used that work under generating conditions. The tool will form the gear tooth; so to produce the specified gear geometry and, especially, the fillet geometry, this tool must be conjugated to the same basic rack as the gear to cut. However, this gives a risk that the tooth tip of the tool will be undercut, and if this occurs the tool will not cut the intended gear fillet. In this report, novel analytical equations are derived, which predict the limit when the tool tip will be undercut. It is shown that if the gear tooth should be conjugated to the standard basic rack with a circular fillet, which is the normal case, very large tool-tooth numbers are needed for pinion shaper cutters and gear skiving cutters to avoid this type of undercut. However, the minimum tooth number to achieve a smooth continuous tool-tooth profile is reduced by modifications to the fillet of the basic rack profile.