Theoretical Investigation of Mesh Relationship and Mesh Stiffness of Internal Spur Gears with Tooth Wear

The internal gear is part of the planetary and epicyclic gear pairs in the transmission system of the helicopter. Gear tooth wear is one of the most usual gear failures. This paper establishes an analytical model to evaluate the influence of tooth wear on the mesh relationship. A new mesh relationship can be derived for internal spur gears with tooth wear by the proposed analytical model. Consequently, using the new mesh relationship, the two most important meshing excitations, mesh stiffness and unloaded static transmission error (USTE), are quantitatively evaluated for the internal gear with tooth wear. The results indicate that tooth wear mainly affects the meshing ranges of single-tooth and double-teeth in mesh stiffness, rather than its amplitude. Additionally, the amplitudes of USTE increase with the increasing wear depth. Finally, this study can offer a foundation for the dynamic modeling and fault diagnosis of internal spur gears with wear faults.