Geometric Characterization and Parameters Selection of Gielis Superformula-Based Pitch Curves for Undercut-Free Noncircular Gears Design

Abstract

The paper is concerned with the insertion of the Gielis’ supershape in the non-circular gears’ theory, by selecting a subset of the modified elliptical shapes to define the pitch curve of the driving gear. A one-factor-at-a-time sensitivity analysis enables a proper selection of the Gielis’ supershape defining parameters, to achieve convex shapes, with maximum curvature limited by the undercutting phenomenon occurring during gear manufacture. A simulation of the gear’s teeth generation wherein a pinion-type shaper cutter serves as a cutting tool, enable to illustrate the tooth flank profile geometry, as a graphical validation of the developed analysis. Manipulating the driving pitch curve geometry, through the Gielis’ superformula parameters, the transmission ratio variation can be easily achieved.