Crowned spur gears for constant mesh stiffness: A conceptual approach

Flank line crowning is a gear surface geometry modification that can be applied as a measure to accommodate contact imperfections along the gear teeth facewidth, that are a consequence of misalignment from either geometric defects or elastic deflection. Due to flank line crowning, the contact stiffness between the teeth of an ideal spur gear changes, thus modifying the gear mesh stiffness. Gear mesh stiffness fluctuations are one of the main driving factors behind gear performance, such as transmission error, dynamic overload and overall system vibration. Regardless of manufacturing feasibility, a set of analytical equations, derived from the classical elliptical contact theory is presented aiming to find the flank line crowning values along the path of contact that eliminate gear mesh stiffness fluctuations. This is achieved by transforming the shape of single teeth pair mesh stiffness through the contact stiffness, making it similar to the shape of the load sharing. A direct method to find the load sharing of spur gears with flank line crowning is also presented.