A hybrid method for mesh stiffness modelling in the presence of structural defects using the finite element method and local slope Approach

Abstract

This work proposes an enhanced hybrid formulation for evaluating the Time-Varying Mesh Stiffness (TVMS) of helical gears in the presence of structural defects. While traditional compliance models often rely on computationally intensive full-scale numerical simulations or oversimplified analytical slicing, this paper introduces a novel extension of the Hybrid Cooley's Approach (HCA) coupled with the Local Slope Method, specifically adapted for helical tooth geometries. The main novelty lies in integrating localized numerical compliance corrections directly into an analytical multi-slice framework, enabling the simultaneous tracking of non-uniform tooth spalling and crack propagation profiles with minimal computational cost. To verify the proposed hybrid formulation and capture localized stress distributions under distinct load configurations, a rigorous three-dimensional Finite Element (FE) model is developed. The comparative outcomes demonstrate that the proposed method effectively bridges the gap between fast analytical routines and high-fidelity numerical solutions, achieving high accuracy in stiffness estimation across varying operational load ranges. This research advances the fundamental understanding of fault-induced vibration behaviors and establishes a precise, computationally lightweight prognostic tool for early fault detection in industrial power transmissions. Conflict of Interest Statement The authors declare no conflicts of interest.