Nonlinear Characterisation of Wind Turbine Gearbox Vibration Dynamics Driven by Inhomogeneous Helical Gear Wear

Helical gear transmissions in wind turbine gearboxes operate under high torque, variable speed, and complex rolling–sliding contact conditions, where friction-induced wear evolves in a spatially non-uniform manner. However, most existing dynamic models assume uniform or mild wear and therefore fail to capture the nonlinear coupling between localised tooth surface degradation, gear mesh dynamics, and vibration response. In this work, a nonlinear dynamic model of a helical gear pair is formulated by incorporating time-varying mesh stiffness, elasto-hydrodynamic lubrication (EHL)-based friction forces, and wear-dependent contact geometry. The governing equations of motion are derived to explicitly account for the influence of inhomogeneous tooth wear on the contact load distribution and frictional excitation during meshing. Wear evolution is represented as a spatially varying modification of tooth surface topology, enabling the progressive coupling between wear depth, mesh stiffness perturbations, and dynamic transmission error. The model is employed to analyse the effects of non-uniform wear on system stability, vibration spectra, and dynamic response under wind turbine operating conditions. Numerical results reveal that uneven wear introduces nonlinear modulation of gear mesh forces and generates characteristic sidebands and amplitude variations in the vibration signal that are absent in conventional mild-wear formulations. These wear-induced dynamic features provide mathematically traceable indicators for the onset and progression of uneven tooth degradation. The proposed framework establishes a physics-based link between wear evolution and measurable vibration responses, providing a rigorous foundation for advanced vibration-based diagnostics and model-driven condition monitoring of wind turbine gearboxes.