Continuous optimization method of micro geometry for unparallel beveloid gears

To enhance the bearing capacity and minimize the loaded transmission error for unparallel beveloid gears, a continuous optimization method of micro geometry is proposed. Considering that the conjugate characteristic of tooth surfaces is destroyed by misalignments and modification, an unload contact analysis model is first developed. This includes a contact tooth sequence determination model and an unloaded transmission error calculation model for multi-tooth contact. To determine contact due to deformation, a potential contact point matching model of non-contact tooth surfaces is introduced. Further, a numerical loaded contact analysis model based on the influence coefficient method for unparallel beveloid gear is developed. For multi-tooth contact of modified tooth surfaces, the transmission error compatibility condition is introduced. Based on the loaded contact model, a continuous optimization model for the comprehensive performance of contact pressures and loaded transmission error within a meshing cycle is established. To improve optimization efficiency, a calculation strategy for continuous optimization is developed. The feasibility of the proposed method is validated using a numerical example.