Mathematical modeling for detecting variable gear tooth cracks in a wind turbine gearbox operating under a ramp-up wind speed

Abstract Wind is natural and possesses renewable energy. This energy is an opportunity when fossil fuel is shrinking very fast and creating heavy ecological imbalance. Wind energy (WE) is an input to wind turbine (WT) system that produces electricity. Therefore, knowledge of wind is a prerequisite for the dynamic modelling of wind turbine drivetrain system (WTDS) in case of defective gear drives. Wind speed is not certain and its ramp-up component can be very detrimental in poor occasions. Input torque to drivetrain system is modelled based on ramp-up wind speed for the diagnosis under healthy and defective WTDS. Lumped parameter model simplifies the mathematical model of gearbox and the Lagrange’s formulation gives insights to derive the equation of motion of the system. Time varying mesh stiffness (TVMS) computed at mean speed is interpolated in MATLAB to get the same at ramp-up condition. The interpolated stiffness is incorporated in the mathematical formulation for both healthy and defective system. Numerical discretization of differential equation is done in MATLAB using Houbolt method to produce the dynamic responses of WTDS with gear defects under ramp-up speed. Here, time frequency (TF) domain analysis is explored to perform dynamic analysis. Hence, short time Fourier transforms (STFT) is applied to low pass filtered signal; wavelet packet transform is helpful in filtering process. The signal processing technique is proposed to investigate the defective WTDS under variable wind speed. This can be helpful in future investigations in WT under more real situations.