scope:

In custom designs of external spur or helical gears, designers generally prefer a lower form diameter for greater transverse contact ratio. A larger root fillet radius and a higher root diameter are also preferred for higher root bending strength. The combination of the above three requirements can render the gear designs unable to be manufactured by hobbing process followed by flank-only finishing processes. To assist gear designers instantly verify the manufacturability of their designs, two methods are presented in this work to calculate the manufactured form diameter given the design parameters of the gear and the hob. In particular, the second method does not involve iterative calculations or graphical simulations which are adopted by numerous publications and software programs. Instead, a series of empirical formulas are provided for users to directly find the manufactured form diameter using the gear design parameters and hob geometries. Over wide ranges of gear design parameters, the formulas can calculate form diameters with relative errors smaller than 0.1%. Examples of applying the formulas are also presented.