An efficient multi-physics computational framework for coupled friction-wear evolution and elastodynamic characterization of helical gears

The evaluation of time-varying mesh stiffness (TVMS) and morphological degradation in helical gears presents a formidable computational challenge due to the intricate multi-physics coupling of lubrication, friction, and wear. To resolve computational bottlenecks, this study proposes an efficient, high-fidelity numerical framework for the coupled friction-wear evolution and elastodynamic characterization of helical gears. A dimension-reduced, semi-analytical axial bending stiffness algorithm is formulated based on a stacked-composite beam analogy, integrated with multi-scale de-formation compatibility equations to track progressive profile deviations. Validation against 3D finite element method (FEM) confirms that the proposed algorithmic solver accelerates the solution process by over 60 times while maintaining high fidelity. Numerical investigations reveal the mechanistic synergy where increments in helix angle and face width dilute the localized load-sharing factor, while an enlarged pressure angle suppresses material removal at the source. Crucially, the solver identifies a spatiotemporal resonance zone at axial contact ratios near unity, where peak wear migrates dynamically toward the trailing end face. Furthermore, a self-adaptive running-in effect and a mechanical inversion in the full elastohydrodynamic lubrication (EHL) regime are elucidated, where load-dependent Hertzian hardening partially compensates for frictional compliance. This computationally efficient approach provides a robust solver architecture for the digital twin modeling and full-lifecycle performance evaluation of spatial transmission systems.