Face Gear Surface Generation with Mathematica

From first principles to surfaces in CAD

Steve Bush

The Procter & Gamble Company

Abstract

A design flow for specifying, analyzing, and exporting face gear tooth surfaces is presented. This process illustrates that Mathematica can be used in the engineering world not only for analytical examination, but also to cross the boundary to the approximate world of CAD and manufacturing. Relying heavily on rotational transforms, a face gear tooth surface can be generated analytically using only a few simple equations. The analytical surface can be analyzed to guide the designer to appropriate tooth sizes and allowable tolerances for gear placement. Finally, the analytical surface can be interpolated using splines, and formatted for delivery in industry standard CAD neutral format.