Geometric design and contact analysis of internal meshing gears with elliptical contact path

This study proposes a design method of internal meshing gear with elliptical contact path, and its contact characteristics are analyzed. The tooth profile of the internal meshing gear is actively designed based on elliptical meshing line (EML). Firstly, the elliptic meshing line is established according to the principle of differential geometry. The intersection points of the index circle and the tooth top circle of the internal meshing gear are on the meshing line. And the length of the minor axis of the elliptical meshing line can be set arbitrarily. Secondly, based on the rack equation and plane coordinate transformation, the tooth top profile equation of the EML gear was derived. Finally, the root tooth profile equations are derived from the top tooth profile equations based on the gear meshing principle. The theoretical model of EML gear is verified by finite element method. The contact stress, meshing stiffness and transmission error of minor axis of elliptic meshing line under different lengths are analyzed. The results show that by adjusting the length of the minor axis appropriately, the contact stress, mesh stiffness and transmission error of the EML gear will be reduced accordingly. Compared with involute gears, the contact stress of EML gears is reduced by 58.76%, the mesh stiffness is increased by 68.38%, and the transmission error is reduced by 40.62%. The contact performance of internal gears is greatly improved. By modifying the minor axis length of the elliptic meshing line of EML gear, the tooth profile of EML gear can be automatically modified through the equation relationship between the minor axis length and the tooth profile, so that the tooth profile design is more efficient. This study provides a reference for improving the performance of internal meshing gears.