Analytical gear mesh stiffness model with hole-induced elastic inhomogeneity

The weight-reduction hole is a critical lightweight design feature in high-power gear transmissions, yet it introduces elastic field inhomogeneity and significantly alters mesh characteristics. The long‑standing difficulty of establishing a unified analytical framework for this issue limits flexible mesh analysis and iterative hole design. This paper proposes an analytical model to directly bridge mesh stiffness and hole-induced elastic inhomogeneity. For the multiply connected elastic domain of a fillet foundation, closed-form hypersingular integral potentials are re‑derived and extended to complex mesh loading conditions. A direct regularization removes the singularities and multivalueness in mixed-boundary equations. Subsequently, a unified fillet foundation stiffness and a full-process load sharing model are formulated to non-recursively capture complex local mesh characteristics across multiple mesh cycles. Besides, the model enables elastic field evaluations for stress analysis and topological optimization. These developments are integrated by a fast computation framework with good numerical properties. Comparisons with benchmark FEM indicate the accuracy in predicting boundary displacements, stress fields, load sharing, and mesh stiffness.