Analytical geometry of straight conical involute gears

Although conical involute gears are frequently used in anti-backlash schemes, no detailed mathematical geometry description of conical involute gear teeth hitherto exists. In this paper we derive the parametric equations for a straight conical involute gear tooth surface and its offset surface. These formulas are then used to create a finite element (FE) model with a specific surface layer. Such a surface layer enables meshing control or modelling of surface properties such as case hardening and surface roughness. In addition, we derive an expression for the minimum value of the inner transverse addendum modification coefficient that avoids undercutting of the whole gear tooth.