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 , and . A novel method to choose cutting parameters and tool design is also presented.
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