A helical gear with discrete ring-involute teeth

This study produces a skewed-imaginary planar rack cutter with discrete conical teeth that is used to create a helical gear with discrete ring-involute teeth. A mathematical equation for the skewed-imaginary rack cutter with discrete conical teeth is firstly solved. The coordinate system for the rack cutter and gear pair is then established and a family of the rack-cutter surfaces is obtained using homogeneous coordinate transformation. The relative velocity method is used to produce the equation for meshing between the rack cutter and the gear pair. Substituting the equation of meshing into the family of the rack-cutter surfaces gives the mathematical models for the gear pair with discrete ring-involute teeth. The transmission error for the gear pair is calculated using the assembly error and a tooth contact analysis. A computer-aided design software package is used to establish solid model for the gear pair. A software interference function is used to simulate the contact condition for the gear pair for various assembly errors. Finite element analysis software is then used to determine the contact stress for the gear pair. The transmission error and the contact stress for the gear pair are insensitive to any horizontal misalignment in the assembly errors.