An efficient semi-analytical loaded tooth contact analysis method for modified face-gear drive using Rayleigh–Ritz approach

The loaded tooth contact analysis (LTCA) is a crucial tool for examining the meshing performance of gear systems. Existing LTCA methods for face-gear drives predominantly rely on finite element method (FEM), which is computationally expensive. To overcome this limitation, a semi-analytical LTCA model is proposed. This model is developed based on deformation compatibility and force equilibrium conditions. The Influence Coefficients Method is used to establish the relationship between contact force and deformation. In this approach, the global tooth deformation compliance is calculated using the Rayleigh–Ritz method, while the local contact deformation compliance is derived from the Boussinesq solution. The semi-analytical LTCA model is solved iteratively to obtain key meshing performance characteristics, such as load distribution, contact pattern, load sharing ratio, and time-varying meshing stiffness. The proposed model is compared with FEM, demonstrating excellent agreement and high computational efficiency. Additionally, parametric analyses reveal that the number of teeth on the shaper, the parabola coefficient of profile crowning, and the output torque significantly affect the meshing performance.