Scrutinising the reliability and dynamic performance of a wind turbine with uncertain interval defects using a bivariate Chebyshev polynomials method

Abstract

Wind turbines operate in severe environments with heavy loads and random factors. Over time, faults such as tooth fractures, errors in planet position, and gear thickness errors will inevitably arise in the system, not to mention the mesh stiffness modelling error. Given the inaccessibility of offshore turbines, fault measurements cannot be modelled using fixed values. To address these challenges, this study evaluates the reliability and dynamic behaviour of the wind turbine gearbox under various interval-based approaches. Specifically, the wind turbine gearbox under study consists of two planetary gears and a high-speed stage gear, with random input torque stemming from aerodynamic wind considered. The modelling approach utilises the potential energy method and Heaviside functions to capture the time-varying mesh stiffness for both external and internal helical gears. To analyse the system under various interval variables, the Bivariate Chebyshev Polynomial Method (BCPM), combined with the least squares technique, is applied. The bounds obtained from BCPM are then validated against some interval-based methods referenced in prior studies. The findings show that BCPM produces precise outcomes with significantly reduced computational effort. Finally, a non-probabilistic reliability analysis assesses system performance under various interval-based faults. The vibration threshold for turbines is established based on Germany’s VDI 3834 Vibration standard. Overall, the reliability analysis in this study highlights the need to implement strategies that enhance system modelling and develop intervention protocols to address system unreliability.