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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.

A parametric mathematical model is presented, by which it is possible to determine the machined gear tooth surface topography cut by a pinion shaper cutter. Arbitrary internal or external helical gears designs can be considered, the gear and the shaper cutter must only share a basic rack design. The basic rack has here an elliptical fillet, as it allows fewer tool tooth numbers without the risk of undercut. The machined tooth surface is presented in three dimensions and by surface roughness parameters [Formula: see text], and [Formula: see text]. A novel method to choose cutting parameters and tool design is also presented.

This paper describes a method to minimize bearing forces as well as bearing and housing mass for a multistage gear reduction. This is done by finding the optimum dog-leg angles for the stages while leaving other aspects of the design unaltered. The optimization is demonstrated first for spur gears, and then for helical gears typically used in electric vehicles. A numerical example shows how bearing forces and mass of bearings and housing are reduced considerably by choosing the optimum dog-leg angle.

No abstract