Analytical Definition and Application of Straight Bevel Gear Tooth Form

Although the methodology of straight bevel gear tooth form generation has been known for quite some time, few references are available in the literature. Presented in this paper are the general numerical procedures of spherical involute and octoid tooth form generations. We have proven that a tooth form generated from the latter approach, by simulating the rotation of a crown gear, matches exactly with the one from the former approach of unwraping a wire from a base circle. The advantage of using general numerical procedures rather than closed form equations is the flexibility of generating both standard and modified gear tooth profiles. In making the forging die, the gear tooth form must be developed with considerations of both the theoretical optimal geometry, and the dimensional compensation for heat treatment distortion. In addition to die design, the gear tooth form is a valuable reference in coordinate measurements for manufacturing process improvement, geometry modeling for finite element stress analysis, forging manufacturing process simulation, and gear friction and lubrication analyses.