Fracture mechanics-based modeling of time-varying mesh stiffness for spiral bevel gears with spatial crack propagation

Spiral bevel gears (SBGs), as critical components in aerospace transmissions, are highly susceptible to crack initiation under heavy-load conditions, which markedly reduces mesh stiffness. This study proposes an innovative analytical framework that merges gear meshing theory with fracture mechanics, transcending the limitations of traditional plane-strain assumptions. First, an accurate conjugate tooth-surface model is constructed on the basis of tool motion derived from meshing theory, and tooth-contact analysis (TCA) is employed to reveal the meshing trajectories and contact characteristics of the gear pair. Second, a coupled slice-potential energy method is introduced to define a pinion crack model for cracks propagating along the tooth width; the model is parameterized by crack depth, crack length, and the angle between the crack and the outer surface, and time-varying mesh stiffness (TVMS) models for both healthy and cracked SBGs are established to uncover the differential effects of varying crack parameters on TVMS degradation. The regulatory laws governing changes in structural parameters-initial meshing phase angle, pitch cone angle, and face cone angle-on contact trajectories, load distribution, and mesh stiffness are systematically analyzed, and the advantages of the proposed method over traditional stress-based approaches are highlighted. Finally, the reliability of the fault stiffness calculation model is verified through finite-element validation and experiments on a cracked-SBG test rig using time-domain and frequency-domain features, providing a theoretical basis for early crack fault diagnosis based on stiffness monitoring.