Deformation overlap in the design of spur and helical gear pair

The elastic deflection of gear teeth is analyzed to investigate the deformation overlap. The deformation overlap, which is a numerically calculated quantity through displacement analysis at the initial contact, is defined as the piled region of a contact tooth pair due to the elastic deformation. The deformation overlap is suggested for an effective indicator to represent the whole deformation of a meshing gear pair. The elastic contact theory and finite element method are used to compute the contact force and teeth deflection. The contact problem is defined as a QP problem, and the contact forces between teeth are calculated from the transmitted torque. Then the deformation overlap is calculated with the contact forces as boundary conditions. For a spur gear pair, the calculated deformation overlap is used for the basis of the tooth tip relief, analysis of deformation characteristics for a profile shifted gear pair, and the selection of profile shift coefficient considering teeth deflection. Deformation overlap is extended to a three-dimensional problem, and implemented to a helical gear pair.

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